EN FRANÇAIS Ce travail porte principalement sur le suivi d'activité physique des personnes âgées en vue de l'analyse de leur trajectoire de fragilisation. Le syndrome gériatrique de fragilité, représenté par un affaiblissement physiologique et la sarcopénie, toucherait 4 personnes sur 5 de plus de 85 ans en France. Des questionnaires et d'autres tests de performance ont été proposés dans la littérature pour évaluer le bien-être des personnes âgées. Ces données étant subjectives et mesurées dans des conditions supervisées à court terme, nous proposons un système de surveillance entièrement automatisé, basé sur des capteurs portables pour faire face à ces problèmes. Ce système se compose de deux couches distinctes : (1) un module de reconnaissance des activitiés physiques, basé sur l'apprentissage automatique pour détecter les activités de la vie quotidienne ADLs (Activities of Daily Living), et (2) une unité de traitement pour analyser les activités détectées et évaluer les conditions de fragilité du senior. La faisabilité et l'efficacité de ce système de surveillance ont été testées en réalisant une série d'expériences.

me. I also want to thank her for the kindness she has shown me, and for all these long discussions and patience to carry out this work.

I would like to express my special thanks to Dr. Majd Saleh, my former colleague at LTSI, for his contribution in enriching this thesis with his experience and suggestions during the first half of my PhD.

I would also like to thank Prof. Jérôme Boudy and Prof. Pierre-Yves Gumery who agreed to report on this thesis. I am very honored.

I would also like to thank Prof. Eric Campo, Prof. Jean-Baptiste Fasquel, Prof. Mohamad Khalil, and Prof. Dominique Somme for having accepted to be part of my defense jury. I am also very honored.

I would also like to thank Prof. Lotfi Senhadji for welcoming me in LTSI and the secretaries Soizic, Patricia and Muriel for their logistical support and sympathy.

Many thanks go to all the ACCORDS project partners, with whom I had the opportunity to share scientific collaborations during all our meetings. This work would not have been done without their contributions and help.

A big thank you goes to all the colleagues, with whom I had the pleasure to have fruitful discussions and to share memorable moments during these past three years.

Finally, it is a privilege to express my sincere appreciation to my parents and my partner, for their continuous support, sacrifices and unconditional love. They have always done their utmost for my success, and I could never express how much I am grateful to them.

Introduction

La première fois dans l'histoire où le nombre de personnes âgées dépassera le nombre de personnes plus jeunes approche rapidement (WHO, 2010), en raison de l'augmentation de l'espérance de vie. Même si la majorité des Français souhaite vieillir à domicile (CSA/FEPEM, 2016), la perte d'autonomie et le risque de chute menacent ce choix de vie. L'enquête SHARE (Survey of Health, Aging and Retirement in Europe) a montré que 15% des personnes âgées de plus de 75 ans sont fragiles, tandis qu'une personne sur cinq âgée de plus de 85 ans est considérée comme robuste [START_REF] Santos-Eggimann | La fragilité en europe : résultats de l'enquete share[END_REF]. Il convient de mentionner que les coûts de santé les plus élevés dans les pays industrialisés sont dus à la consommation médicale des personnes âgées fragiles [START_REF] Fassbender | Cost trajectories at the end of life: the canadian experience[END_REF], car la fragilité se manifeste par un déclin désastreux de la fonction physique et augmente la vulnérabilité. Par conséquent, la prévention de la fragilité est une priorité actuelle de l'Organisation Mondiale de la Santé et devient un sujet d'attention pour les décideurs publics. Par suite, il en résulte un besoin urgent de suivi continu de l'activité sans hospitalisation.

Cette thèse s'inscrit dans le cadre du projet ANR ACCORDS (Approche Combinatoire de fonctionnalités COnnectées pour le Recueil de Données de Santé à visée multimodale). Le CHU de Rennes est le promoteur de cette étude, qui est coordonnée par le Laboratoire Traitement du Signal et de l'Image (LTSI), Inserm U1099, Université de Rennes 1. Ce projet réunit deux qu'un compteur de pas porté au poignet. Une application mobile dénommée "Calliopé" a été développée par AZNetwork. Cette application a été installée sur une tablette pour communiquer avec les capteurs susmentionnés et illustrer les données acquises (poids, pression sanguine, pas) qui sont envoyées et stockées sur le serveur sécurisé d'AZNetwork. Un autre dispositif portable, composé de différents capteurs permettant de collecter des données brutes (telles que l'accélération et la pression atmosphérique), a été développé par RF-Track. La Figure 1 illustre les différents éléments résumant le projet ACCORDS. Ces données sont traitées pour quantifier l'activité physique du porteur du dispositif. Ce projet vise également à (i) évaluer l'acceptabilité de cette plateforme (incluant les dispositifs portables) par les personnes âgées (étude menée par le CIC-IT de Rennes), et (ii) proposer des algorithmes intelligents (étude menée par le LTSI) exploitant les données acquises par les capteurs portables afin de détecter et de surveiller l'activité physique pour l'évaluation et l'analyse de la fragilité des personnes âgées. La détection précoce de la fragilité devrait alors être envisageable.

Health Monitoring

© Calliopé by AZNetwork

Dans le cadre de cette thèse, il s'agit d'étudier la faisabilité de quantifier l'activité physique à partir de capteurs portables pour une potentielle détection précoce de la fragilité. Notre objectif se décompose en deux étapes : (a) l'identification des activités effectuées par le sujet, et (b) l'analyse des mouvements pour évaluer son état physique. Les principales contributions de ce travail sont les suivantes :

• Revue de la fragilité d'un point de vue médical afin d'introduire la formulation du problème (section 1, intitulée « Contexte médical et énoncé du problème »)

• Exploration des composants du système de surveillance en termes de matériel et logiciel informatique et conception de deux bases de données créées par notre équipe pour développer et valider nos techniques (section 2, intitulée « Choix du système de télésurveillance »)

• Proposition de différentes méthodes de détection automatique des activités physiques (section 3, intitulée « Reconnaissance des activités physiques »)

• Proposition de caractéristiques symbolisant la fonction physique du senior, afin d'évaluer l'état de fragilité (section 4, intitulée « Analyse de la fragilité »).

Contexte médical et énoncé du problème

La fragilité peut être définie comme un déclin du fonctionnement de plusieurs systèmes physiologiques, accompagné d'une vulnérabilité accrue aux facteurs de stress [START_REF] Hoogendijk | Frailty: implications for clinical practice and public health[END_REF]. La Figure 2 illustre le modèle de cette maladie et ses différentes étapes. La personne âgée passe par quatre niveaux : (a) robuste (robust), (b) pré-fragile (pre-frail), (c) fragile (frail), et (d) état de handicap (disability). L'état de pré-fragilité peut être atténué ou réversible par des interventions médicales, c'est-à-dire que la personne âgée peut retrouver ses capacités physiques.

En théorie, il en va de même pour l'état de fragilité, même s'il n'existe pas de consensus pour la réversibilité de cet état. Cependant, la transition vers l'état de handicap est difficilement réversible, voire irréversible. De plus, il a été démontré que la fragilité augmente le risque de chutes, de manque d'autonomie et d'hospitalisation [START_REF] Rockwood | Frailty in relation to the accumulation of deficits[END_REF]Strandberg et Pitkälä, 2007). Une approche largement utilisée pour définir la fragilité a été élaborée par Fried et al., et repose sur un phénotype spécifique [START_REF] Fried | Frailty in older adults: evidence for a phenotype[END_REF]. Ainsi, la fragilité est caractérisée comme un syndrome clinique répondant à au moins trois critères sur cinq parmi les critères suivants : (i) perte de poids involontaire, (ii) fatigue autodéclarée, (iii) faiblesse (au 65 100

Age

Frailty

• Pre-Frail

Robustness Disability Performance

• Frail

Figure 2 -Les différents stades du modèle de fragilité avec les courbes de vieillissement en fonction de l'âge (vieillissement normal et accéléré). niveau de la force de préhension), (iv) vitesse de marche ralentie et (v) faible activité physique (en utilisant un questionnaire). Les personnes âgées ne présentant aucun de ces cinq critères sont classées comme robustes, tandis que celles présentant un ou deux critères sont considérées comme pré-fragiles. Ce phénotype a été testé dans le cadre de l'étude « Cardiovascular Health Study » [START_REF] Fried | Frailty in older adults: evidence for a phenotype[END_REF]. On a observé que la fragilité augmente avec l'âge et qu'elle touche les femmes plus que les hommes. En outre, un état de pré-fragilité (1 ou 2 critères) augmente le risque de devenir fragile au cours des 3-4 années suivantes.

Les recherches et les études se sont multipliées pour trouver des approches et des modèles en vue de l'analyse de la fragilité et de l'évaluation de la fonction physique. Tout d'abord, des données mesurées subjectivement, des questionnaires d'auto-évaluation et d'autres tests de performance ont été proposés pour évaluer les conditions physiques et le statut de fragilité des personnes âgées. En plus du phénotype de fragilité [START_REF] Fried | Frailty in older adults: evidence for a phenotype[END_REF], le test SPPB (Short Physical Performance Battery) [START_REF] Guralnik | A short physical performance battery assessing lower extremity function: association with self-reported disability and prediction of mortality and nursing home admission[END_REF], qui est un mélange de trois tests, a été développé pour évaluer la force musculaire, l'équilibre et la mobilité du senior. En outre, le questionnaire PSQI (Pittsburgh Sleep Quality Index) [START_REF] Buysse | The pittsburgh sleep quality index: a new instrument for psychiatric practice and research[END_REF] est un questionnaire qui a été conçu pour mesurer la qualité du sommeil.

La relation entre les biomarqueurs et la fragilité a été abordée dans la littérature. Les marqueurs inflammatoires, comme la protéine C-réactive et l'interleukine-6, qui augmentent avec l'âge [START_REF] Ferrucci | The origins of age-related proinflammatory state[END_REF], ne se sont pas révélés être des prédicteurs fiables de la transition vers la fragilité [START_REF] Puts | Endocrine and inflammatory markers as predictors of frailty[END_REF][START_REF] Reiner | Inflammation and thrombosis biomarkers and incident frailty in postmenopausal women[END_REF]. Par ailleurs, les marqueurs métaboliques, notamment l'hémoglobine glyquée HbA 1C , ont également fait l'objet de plusieurs études.

Des niveaux très bas de HbA 1C ont été liés à un risque accru de chutes et de mortalité chez les personnes fragiles (Abdelhafiz et Sinclair, 2015 ;[START_REF] Nelson | The relationship between glycemic control and falls in older adults[END_REF]. Néanmoins, sa capacité à détecter la transition entre les trois classes de fragilité reste discutable. De plus, les chercheurs doutent que la testostérone puisse être utilisée comme outil de dépistage de la fragilité, étant donné qu'il existe un petit nombre de preuves suggérant une corrélation entre ce changement hormonal et la trajectoire de la fragilité [START_REF] Carcaillon | Sex differences in the association between serum levels of testosterone and frailty in an elderly population: the toledo study for healthy aging[END_REF][START_REF] Hyde | Low free testosterone predicts frailty in older men: the health in men study[END_REF].

Plus récemment, certains travaux ont consisté en des études observationnelles en surveillant un ensemble de différentes métriques d'activité à partir de capteurs portables en relation avec le statut de fragilité et l'état de santé du senior. Un capteur suspendu a, par exemple, été utilisé pour surveiller l'activité physique de personnes âgées (≥ 60 ans) pendant 48 heures, en observant la posture corporelle (marcher, s'asseoir, se tenir debout), le comportement d'activité (sédentaire, légère, modérée à vigoureuse), le nombre de pas et la qualité du sommeil [START_REF] Razjouyan | Wearable sensors and the assessment of frailty among vulnerable older adults: an observational cohort study[END_REF]. Cette étude a été étendue à l'évaluation de la fragilité cognitive chez les personnes âgées vivant en communauté [START_REF] Razjouyan | Toward using wearables to remotely monitor cognitive frailty in community-living older adults: an observational study[END_REF], en considérant des caractéristiques comme des paramètres liés au sommeil, les périodes de marche et le nombre de pas. Une autre recherche a eu lieu pour évaluer la fiabilité des dispositifs portables pour l'évaluation de la fragilité à domicile [START_REF] Kim | Consumer-grade wearable device for predicting frailty in canadian home care service clients: prospective observational proof-of-concept study[END_REF]. Les données acquises auprès de participants âgés de 55 ans et plus ont été exploitées pour dériver des variables comprenant le nombre de pas quotidiens, le temps et la qualité du sommeil et la fréquence cardiaque sur une période de 9,43 (± 1,99) jours. En outre, et puisque la fragilité est l'un des principaux facteurs de risque de chute chez les personnes âgées [START_REF] Clegg | Frailty in elderly people[END_REF][START_REF] Rockwood | Frailty in relation to the accumulation of deficits[END_REF], des systèmes de détection automatique des chutes ont été développés, garantissant une intervention médicale opportune. La détection des chutes a fait l'objet de nombreuses recherches au cours des dernières décennies [START_REF] Charlon | Design and evaluation of a device worn for fall detection and localization: application for the continuous monitoring of risks incurred by dependents in an alzheimer's care unit[END_REF]Thome et al., 2008), et reste un domaine de recherche actif [START_REF] Saleh | Elderly fall detection using wearable sensors: a low cost highly accurate algorithm[END_REF]G. Wang et al., 2020 ;[START_REF] Zhong | Multi-occupancy fall detection using non-invasive thermal vision sensor[END_REF].

Malgré les efforts et les approches développés pour détecter et analyser le syndrome de fragilité chez les personnes âgées, il existe encore un certain nombre de limitations qu'il convient de mentionner. Bien que les critères du phénotype de fragilité déterminent le statut de fragilité dans un contexte clinique à un moment donné, leur efficacité est limitée lorsqu'il s'agit de prédire et d'identifier la progression de la robustesse vers la fragilité. En outre, la capacité des questionnaires et des tests de performance à suivre la trajectoire de la fragilité est discutable dans la mesure où (i) ils sont basés sur des mesures subjectives, (ii) ils sont effectués dans des conditions supervisées et (iii) ces tests fournissent une estimation à court terme des capacités physiques à un moment donné. De même, malgré les tentatives déployées pour analyser ce syndrome à l'aide de capteurs portables, de larges ensembles de variables restent nécessaires, et les chercheurs doivent encore déterminer les critères les plus utiles pour quantifier l'activité physique des personnes âgées [START_REF] Mc Ardle | Quantifying physical activity in aged residential care facilities: a structured review[END_REF]. À ce jour, les caractéristiques les plus pertinentes/discriminantes ne sont pas connues, et la question de savoir si elles dépendent du sujet reste ouverte. De plus, la plupart des expériences inclut des volontaires relativement jeunes (moins de 65 ans) [START_REF] Kim | Consumer-grade wearable device for predicting frailty in canadian home care service clients: prospective observational proof-of-concept study[END_REF][START_REF] Razjouyan | Wearable sensors and the assessment of frailty among vulnerable older adults: an observational cohort study[END_REF] et implique une évaluation à court terme [START_REF] Kim | Consumer-grade wearable device for predicting frailty in canadian home care service clients: prospective observational proof-of-concept study[END_REF][START_REF] Razjouyan | Wearable sensors and the assessment of frailty among vulnerable older adults: an observational cohort study[END_REF][START_REF] Razjouyan | Toward using wearables to remotely monitor cognitive frailty in community-living older adults: an observational study[END_REF][START_REF] Rosenberger | Twenty-four hours of sleep, sedentary behavior, and physical activity with nine wearable devices[END_REF]) (de l'ordre de 24-48 h à quelques jours). En outre, le fait de chuter fréquemment signifie que le sujet est déjà vulnérable ou fragile. L'objectif est donc de prévenir les chutes plutôt que de les détecter, afin d'éviter leurs conséquences et d'interrompre la progression vers la fragilité. Compte tenu des inconvénients susmentionnés, la fragilité reste un défi de recherche ouvert et un domaine actif à ce jour. Le présent travail vise à développer un système de télésurveillance basé sur des capteurs portables en vue de l'analyse de la fragilité. Étant donné que la fonction physique est liée à ce syndrome (contrairement aux biomarqueurs et aux changements hormonaux par exemple), l'approche proposée assure une surveillance continue de l'activité pour la détection précoce de la fragilité. L'objectif est de trouver les indicateurs les plus pertinents pour la détection de l'affaiblissement physique.

Choix du système de télésurveillance

Comme indiqué précédemment, les travaux actuels sont basés sur des capteurs portables. En termes de confidentialité, les capteurs portables ne révèlent pas l'identité du sujet et présentent donc un avantage par rapport aux enregistreurs vidéo. De plus, étant donné qu'ils sont portés sur le corps, ils fournissent des données partout et en permanence, contrairement aux capteurs externes qui souffrent de problèmes de visibilité et sont limités à certains environnements.

a) Les capteurs et leur emplacement

Les capteurs portables miniaturisés sont des outils propices à tout système de reconnaissance d'activités. Le capteur le plus utilisé est l'accéléromètre tri-axial. En général, deux types d'accéléromètres sont déployés dans les trackers portables, à savoir (a) les microsystèmes électromécaniques MEMS (Micro-Electro-Mechanical Systems) et (b) les systèmes piézoélectriques PEC (PiezoElectriC). La Table 1 résume les avantages d'un type par rapport à l'autre (Albarbar et Teay, 2017 ;[START_REF] Di Pietro | Capacitive mems accelerometer for condition monitoring[END_REF]TE Connectivity, 2017 ;[START_REF] Vectornav | Accelerometer[END_REF][START_REF] Wagner | Piezoelectric accelerometers theory and application[END_REF]. Sur la base de cette comparaison, les MEMS ont été retenus dans notre cas. Le deuxième capteur largement utilisé est le gyroscope tri-axial, qui mesure la vitesse angulaire. Couplé à un accéléromètre, il constitue avec ce dernier une centrale inertielle IMU (Inertial Measurement Unit), capable de surveiller les mouvements de translation et de rotation. Ici, le nombre de degré de liberté DoF (Degree of Freedom) augmente de trois à six. Néanmoins, les gyroscopes nécessitent une consommation d'énergie très élevée par rapport aux accéléromètres (Q. [START_REF] Liu | Gazelle: energy-efficient wearable analysis for running[END_REF]. En effet, le courant moyen consommé par le gyroscope peut être dix à cent fois supérieur à celui consommé par l'accéléromètre pour une même fréquence d'échantillonnage (F s ). Le magnétomètre tri-axial est un troisième capteur bien connu, qui est également utilisé dans un large éventail de systèmes de surveillance. Ce dispositif mesure le champ magnétique ou le moment dipolaire magnétique, notamment le champ magnétique terrestre. Par conséquent, en ajoutant le magnétomètre à une IMU, nous créons un système inertiel à 9 DoFs appelé MARG (Magnetic, Angular Rate, Gravity). Ce type d'unité de détection présente l'avantage de mesurer l'attitude par rapport au champ magnétique de la terre. Néanmoins, sa fiabilité dans les environnements intérieurs peut être affectée, étant donné que les champs magnétiques artificiels créés par les appareils électroniques ainsi que les infrastructures mécaniques et électriques contaminent les mesures du champ magnétique terrestre. Enfin, le baromètre est un autre capteur qui peut être utilisé dans un système inertiel. Cet instrument mesure la pression atmosphérique dans un certain environnement, ainsi que la température. Alors que les trois premiers capteurs sont utilisés pour suivre le mouvement de l'unité de détection portable dans un espace tridimensionnel, le baromètre est utilisé comme élément complémentaire pour estimer l'altitude du dispositif. En se basant sur les descriptions précédentes, nous concluons qu'un système inertiel est généralement (i) un système 3-DoF, i.e. basé sur un accéléromètre tri-axial, (ii) un système 6-DoF, i.e. basé sur une IMU (accéléromètre tri-axial + gyroscope tri-axial), ou (iii) un système 9-DoF, i.e. un capteur MARG (IMU + magnétomètre tri-axial). Un baromètre peut être ajouté à l'un des trois systèmes inertiels pour estimer l'altitude du dispositif portable. Le choix des capteurs employés dépend de l'application et du compromis entre la consommation énergétique et la précision.

Plusieurs emplacements ont été envisagés dans la littérature pour les capteurs portables, comme la taille, la poitrine, le bas du dos, le poignet, la cuisse, la cheville etc. [START_REF] Bonomi | Detection of type, duration, and intensity of physical activity using an accelerometer[END_REF][START_REF] Gjoreski | Accelerometer placement for posture recognition and fall detection[END_REF][START_REF] Parkka | Activity classification using realistic data from wearable sensors[END_REF][START_REF] Yeoh | Ambulatory monitoring of human posture and walking speed using wearable accelerometer sensors[END_REF]. En outre, certaines approches utilisent plusieurs capteurs placés sur différentes parties du corps [START_REF] Bharti | Human: complex activity recognition with multi-modal multi-positional body sensing[END_REF][START_REF] Shoaib | Complex human activity recognition using smartphone and wrist-worn motion sensors[END_REF]. Dans notre travail, la télésurveillance est envisagée à partir d'un seul dispositif portable. Ce choix a été imposé dans le cadre du projet ACCORDS à des fins d'acceptabilité. L'emplacement du capteur est un facteur important qui affecte la mise en oeuvre des techniques de détection des activités, ainsi que leur fiabilité et leur précision. Il convient de mentionner que les signaux d'accélération, en général, augmentent en amplitude de la tête à la cheville [START_REF] Mathie | Accelerometry: providing an integrated, practical method for long-term, ambulatory monitoring of human movement[END_REF]. Par conséquent, les capteurs portés à la cuisse et à la cheville sont très sensibles aux mouvements humains, c'est-à-dire que des pics élevés peuvent apparaître même en cas de mouvements d'intensité relativement faible. Ce phénomène peut conduire à une surestimation de certains paramètres basés sur l'accélération, ce qui peut fausser les résultats. De même, bien que les personnes âgées préfèrent en général les trackers portés au poignet à d'autres dispositifs [START_REF] Mercer | Acceptance of commercially available wearable activity trackers among adults aged over 50 and with chronic illness: a mixed-methods evaluation[END_REF][START_REF] Puri | User acceptance of wristworn activity trackers among community-dwelling older adults: mixed method study[END_REF], les données acquises par les dispositifs portés au poignet pourraient être trompeuses pour les unités de traitement. Le poignet n'est pas fixe et bouge dans différentes directions, même pour une même activité. En outre, certains mouvements complexes et/ou inattendus pourraient être effectués. Le dispositif porté au poignet peut être facilement considéré comme l'un des dispositifs les moins précis lorsqu'il est testé sur plusieurs algorithmes basés sur l'apprentissage automatique [START_REF] Cleland | Optimal placement of accelerometers for the detection of everyday activities[END_REF]. Par conséquent, le tronc du corps humain (poitrine et taille) est l'emplacement le plus approprié pour cette tâche. Les données acquises à partir de cette position ne sont pas sensibles aux mouvements de faible intensité, mais leur magnitude est suffisamment importante pour permettre le calcul de caractéristiques informatives. De plus, les positions telles que la poitrine et la taille sont proches du centre de gravité du corps. C'est un avantage pour l'analyse de la fragilité, car l'examen des mouvements du tronc est ce qui compte le plus, surtout lorsqu'il s'agit d'activités comme les transitions posturales (s'asseoir ou se lever) et les mouvements récurrents comme la marche et le jogging. Il est donc logique de considérer le tronc comme emplacement du capteur dans notre travail. Néanmoins, le poignet sera également considéré dans la section suivante pour appuyer les points déjà évoqués.

b) Conception de deux bases de données

Des données sont nécessaires lors du développement d'approches basées sur l'apprentissage automatique et pour mener des études statistiques. En conséquence, nous avons construit deux bases de données différentes, qui servent les deux objectifs principaux de ce travail. La première est dédiée au développement des techniques de la détection des activités et s'appelle FallAllD.

La seconde est dédiée à l'analyse de la fragilité et s'appelle ActFreeLi.

FallAllD : le nom est dérivé de l'expression « Fall in All Directions ». Il s'agit d'un ensemble de signaux représentant des chutes et des ADLs, acquis par notre équipe [START_REF] Saleh | Fallalld: an open dataset of human falls and activities of daily living for classical and deep learning applications[END_REF].

Cette base de données est composée de 26420 fichiers. RF-Track, notre partenaire industriel, a développé trois enregistreurs de données identiques (portés en médaillon, à la ceinture et au poignet) pour recueillir les signaux. Ils se composent d'une IMU (F s = 238 Hz), d'un magnétomètre tri-axial (F s = 80 Hz) et d'un baromètre (F s = 10 Hz). Les participants ont porté les trois dispositifs simultanément et ont simulé une série de chutes et d'activités. En ce qui concerne les chutes, plusieurs scénarios ont été envisagés, caractérisés par différentes postures pré-impact (assis, debout, allongé, en mouvement), différentes raisons de chute (trébuchement, glissade, syncope), différentes directions (avant, arrière, latérale) et différentes postures post-impact (assis, couché). Quant aux ADLs, trois catégories ont été prises en compte, à savoir les mouvements cycliques (tels que la marche, le jogging, la montée/descente d'escaliers), les activités transitoires (telles que s'asseoir, se lever, se coucher, sauter, etc.) et les gestes de la main (tels que applaudir, lever le bras, serrer la main, etc.).

ActFreeLi : le nom est dérivé de l'expression « Activities in Free Living Conditions ». RF-Track a également développé un dispositif portable composé d'un accéléromètre du type MEMS (LIS3DH de STMicroelectronics) et d'un baromètre (MS5611-01BA03 de TE Connectivity). La carte du circuit est encapsulée dans un boîtier qui peut être porté autour du cou ou à la taille (tronc du corps). Les données brutes des deux capteurs sont prétraitées par le microcontrôleur STM32L431 de STMicroelectronics.

Dans un projet précédent appelé Silver@Home, la détection des chutes a été abordée. L'objectif était de développer un détecteur automatique de chute, dédié aux personnes âgées fragiles et susceptibles de tomber. Les données des participants âgés de plus de 80 ans, résidant dans différents établissements d'hébergement pour personnes âgées dépendantes (EHPAD) en France, ont été recueillies. Chaque participant a été suivi pendant 3 mois. Ces expériences ont duré de mai 2019 à mars 2020.

Dans le cadre du projet ACCORDS, une autre cohorte est ciblée, notamment des personnes âgées de plus de 80 ans en meilleure santé et résidant à domicile (appartement ou résidence autonomie). L'idée est de suivre 30 participants recrutés pendant 2 ans (24 mois M 1,...,24 ), afin de définir et de suivre la trajectoire de fragilisation (la transition vers la fragilité). Les expérimentations étaient censées commencer en Mars 2020, mais ont été reportées de 6 mois (Septembre 2020) à cause de la pandémie du coronavirus. Les participants sont visités trois fois au cours de ces 2 années (à M 1 , M 12 et M 24 ) par un spécialiste en psychologie afin d'évaluer leur santé psycho-cognitive et l'acceptabilité du système de monitoring. De plus, ils sont visités tous les 3 mois par un gériatre, dont la tâche est d'évaluer leur état de santé. Lorsqu'un sujet est caractérisé comme étant fragile par le gériatre (en se basant sur le score du phénotype de fragilité développé par Fried et al.), il est exclu de l'étude en cours d'expérience.

Dans les deux projets, les participants ont porté le dispositif au cours de leur routine quotidienne sans aucune instruction spécifique. Les données acquises, qui sont enregistrées sur une carte µSD, sont découpées et stockées sous forme de fichiers de 24 heures. L'utilisation des don-nées des personnes fragiles a été approuvée par le comité d'éthique du CHU de Rennes, tandis que l'utilisation des données recueillies dans le cadre du projet ANR a été approuvée par le comité de protection des personnes (CPP) Ouest VI du CHU Morvan de Brest.

Reconnaissance des activités physiques

Dans un premier temps, nous avons considéré un dispositif porté au poignet qui faisait l'objet d'une étude parallèle sur la détection des chutes (celle du projet Silver@Home) pour détecter l'activité physique. Nous avons proposé une solution peu coûteuse et particulièrement adaptée pour les activités cycliques. Si nos résultats expérimentaux ont permis d'attester l'efficacité de l'approche en conditions supervisées, un tel dispositif s'avère insuffisant pour le dépistage de la fragilité en conditions réelles. Par conséquent, nous avons envisagé deux autres approches et al., 2017), mHealth [START_REF] Banos | Mhealthdroid: a novel framework for agile development of mobile health applications[END_REF][START_REF] Banos | Design, implementation and validation of a novel open framework for agile development of mobile health applications[END_REF], HAPT (Anguita et al., 2013), et UMAFall [START_REF] Casilari | Umafall: a multisensor dataset for the research on automatic fall detection[END_REF]. Cette opération révèle si la méthode proposée est exposée au surapprentissage (overfitting) ou non, en testant le modèle sur de nouvelles données

b) Analyse de la marche

La vitesse de la marche a été proposée comme l'un des critères de fragilité [START_REF] Fried | Frailty in older adults: evidence for a phenotype[END_REF].

Néanmoins, la marche est une activité complexe et ne peut être limitée à une seule variable.

D'autres paramètres liés à la marche peuvent varier au cours de la transition vers la fragilité.

C'est pourquoi six caractéristiques sont proposées, afin de déterminer si la façon de marcher de la personne reflète sa condition physique. L'objectif est l'extraction de variables à partir du module de l'accélération ||a|| et de la composante verticale a X . La Figure 10.a illustre trois modules de l'accélération, chacun associé à un sujet appartenant à l'une des trois populations : Ainsi, V 3 est égale à l'entropie des coefficients d'autocorrélation. Ensuite, la Variable V 4 est égale au nombre de fois où la valeur absolue de la différence entre deux points consécutifs du module ||a|| dépasse un seuil prédéfini (par exemple 0,075g). Cette variable reflète, d'une certaine manière, la variabilité des séries temporelles représentant la marche de la personne. Enfin, les deux dernières caractéristiques représentent le processus de variation temporelle de la marche.

(i) Robuste, (ii) Pré-fragile, et (iii) Fragile. La Variable V
Les coefficients φ i du modèle autorégressif ajusté à la composante verticale a X sont estimés (Neumaier et Schneider, 2001). La Variable V 5 est égale à l'écart-type de φ i , tandis que la Variable V 6 est égale au kurtosis de ces coefficients.

L'objectif est maintenant de combiner les six paramètres de marche proposés en un seul vecteur et d'appliquer un classifieur d'apprentissage automatique pour stratifier les personnes âgées en trois classes (robuste, pré-fragile et fragile). Les caractéristiques susmentionnées varient en termes d'unité et d'amplitude. Elles sont donc mises à l'échelle à l'aide de la fonction sigmoïde.

En plus des sujets recrutés dans ActFreeLi, des données de la base publique de données WWBS Metrics [START_REF] Orselli | Wwbs metrics[END_REF] du projet FrailSafe ont été ajoutées. Les mêmes classifieurs de la sous-section précédente ont été testés. La Table 6 illustre les résultats des différents classifieurs. SVM est le plus performant avec une précision moyenne égale à 88,5%, suivi de NN (88,18%) et du GBM (87,51%). La Figure 11 illustre la matrice de confusion, basée sur la sortie de SVM, dans laquelle les colonnes représentent la classe cible tandis que les lignes représentent les sorties de l'algorithme. 86,6% des signaux de marche appartenant à des sujets pré-fragiles sont bien classés.

En revanche, 11,3% de signaux appartenant à des sujets pré-fragiles sont classés comme robustes et les 2,1% restants comme fragiles. La plus grande confusion se produit au niveau de la classe pré-fragile. En plus de la confusion de 11,3%, 5% des signaux liés à la population robuste et 8,4% des signaux liés à la population fragile sont classés comme pré-fragiles. Ces résultats montrent que la manière de marcher est un bon indicateur de la fragilité (avec une précision entre 88-89%), puisque la matrice de confusion résultante est bien corrélée avec la fragilité phénotypique, ce qui prouve l'efficacité des paramètres proposés. De plus, les déviations par rapport aux classes cibles doivent être considérées comme des indices importants et utiles dans la trajectoire de la fragilité. Les sujets classés comme robustes par le phénotype de fragilité mais considérés comme pré-fragiles par la technique d'analyse de la marche proposée, pourraient être en train de se fragiliser. Cette stratégie pourrait être l'une des bases des futurs systèmes de prévention.

Conclusion

Notre recherche s'est principalement concentrée sur la surveillance de l'activité physique des personnes âgées afin d'évaluer les conditions de fragilité dans des conditions non supervisées.

INTRODUCTION

The first time in history when the number of elderly will exceed the number of younger people is rapidly approaching (WHO, 2010), due to rising life expectancy. As of January 2020, 9.5% of the French population were aged over 75 years old (INSEE, 2020). In less than 40 years, this proportion will increase to 16.2% according to the French National Institute for Statistics and Economic Studies (INSEE, 2010). This justifies why tele-surveillance systems and platforms were discussed in the literature to monitor physiological signals and parameters such as heart rate and body temperature [START_REF] Baldinger | Tele-surveillance system for patient at home: the mediville system[END_REF][START_REF] Jamin | An aggregation plateform for iot-based healthcare: illustration for bioimpedancemetry, temperature and fatigue level monitoring[END_REF]. Even though the majority of French people would like to age at home (CSA/FEPEM, 2016), progressive physical weakening, lack of autonomy and risk of falls threaten this lifestyle choice. The Survey of Health, Aging and Retirement in Europe (SHARE) has shown that 15% of people over 75 years old are 'frail', whereas 1 out of 5 people over 85 years old is considered as robust (Santos-Eggimann, 2013).

It is worth mentioning that the highest healthcare costs in industrialized countries are due to medical consumption of frail seniors [START_REF] Fassbender | Cost trajectories at the end of life: the canadian experience[END_REF], since frailty manifests disastrous declines in physical function and increases vulnerability. Therefore, the frailty prevention is an actual world health organization priority and is becoming a subject of attention for public policy makers. In other words, one of the main stakes in the early future of our society facing the demographic shift is the promotion of healthy aging, leading to an urgent need of continuous activity tracking without hospitalization.

Why Activity Tracking?

Generally, old people who are physically active have better biomarker profiles to prevent certain diseases like cardiovascular disease and type 2 diabetes, and to enhance the bone health (WHO, 2020). Moreover, exhibiting higher levels of physical activities helps to lower the risk of falling and keeping the elderly independent, reverse some effects of chronic diseases, and preserve the cognitive function [START_REF] Mcphee | Physical activity in older age: perspectives for healthy ageing and frailty[END_REF]. Furthermore, the number of steps per day is associated with the risk of mortality in an inversely proportional relationship (NIH, 2019), and seems more important than the step intensity (NIH, 2020;[START_REF] Saint-Maurice | Association of Daily Step Count and Step Intensity With Mortality Among US Adults[END_REF]. However, it is never too late to begin to be active: even in poorly active elderly, the promotion of physical activity is more efficient than educational program [START_REF] Pahor | Impact and lessons from the lifestyle interventions and independence for elders (life) clinical trials of physical activity to prevent mobility disability[END_REF]. Furthermore, it is worth mentioning that stressful life events, anxiety, and depression could harm the physical and mental health, leading to the loss of autonomy. Hence, monitoring the sleep pattern is another important factor, since it is correlated to the quality of life of elderly (Tel, 2013). Additionally, insufficient sleep leads to poor physical conditions and mental impairment. Besides, the reduction of leisure activities and instrumental activities of daily living is mainly associated to the functional capabilities limitations [START_REF] Chattu | The global problem of insufficient sleep and its serious public health implications[END_REF]. Consequently, it is important to observe whether the subject quits his home (house or apartment) frequently or not, taking the lift and/or stairs. This justifies why the detection and surveillance of Activities of Daily Living (ADLs) is the cornerstone of healthcare systems.

ANR ACCORDS Project

This thesis takes place in the ANR ACCORDS project, "Approche Combinatoire de fonctionnalités COnnectées pour le Recueil de Données de Santé à visée multimodale", which stands for combinatorial approach of connected devices to collect multimodal health data. The CHU (Centre Hospitalier Universitaire) de Rennes is the promoter of the study, which is coordinated by the Laboratoire Traitement du Signal et de l'Image (LTSI), Inserm U1099, Université de Rennes 1. It brings together two industrial partners, namely RF-Track (located in Cesson-Sévigné, France) and AZNetwork (located in Alençon, France), as well as the CIC-IT (Centre d'Investigation Clinique -Innovation Technologique) of Rennes. The ACCORDS project aims to set up a telemonitoring solution that responds, on the one hand, to the problems encountered by senior citizens and their family members in terms of health monitoring, and on the other hand, to the social problems linked to the population aging, i.e. finding alternatives to keep older people at home. Hence, based on acquired data, the transition from curative to preventive health model is ensured. The idea is to create a multimodal platform designed to detect the frailty trajectory. This platform includes a set of connected devices, namely a weight scale and a blood pressure monitor (vital signs), as well as a wrist-worn step counter. A mobile application called "Calliopé" was developed by AZNetwork. This application was installed on a tablet to communicate with the aforementioned sensors and to illustrate acquired data (weight, blood pressure, steps) which are sent and stored on AZNetwork secure server. Furthermore, another wearable device, consisting of different sensors to collect raw data (such as acceleration and atmospheric pressure), was developed by RF-Track alongside the aforementioned equipment. These data are processed to quantify the physical activity of the device wearer. This project also aims to (i) evaluate the acceptability of this platform (including wearable devices) by the elderly (study conducted by the CIC-IT of Rennes), and (ii) propose intelligent algorithms (study conducted by the LTSI) exploiting data acquired from wearable sensors in order to detect and monitor the physical activity for frailty assessment and analysis in community-dwelling elderly people.

The early stage frailty detection should then be conceivable. Figure 1 illustrates the different elements summarizing the ACCORDS project.

Health Monitoring

© Calliopé by AZNetwork

Objective and Main Contributions

The objective of this thesis fits well in this scenario. Particularly, the goal is to study the feasibility of physical activity quantification from wearable sensors for frailty early detection.

The aforementioned aim of this work is done in two steps: (a) activity identification, and (b) further movements analysis. Generally, gesture recognition is done using accelerometers, gyroscopes, and magnetometers. Moreover, altitude is estimated using barometers, which measure the atmospheric pressure. It is worth mentioning that these sensors are usually cheap and easily embedded. Once detected and localized, the ADLs are subject to further processing in order to inspect the correlation between extracted features from windowed data and the healthy/frailty status of elderly. Nevertheless, many difficulties arise when developing such an approach. They are related to (i) some artifacts linked to some disturbances, (ii) power consumption which affects the battery life and thus the acceptability of the system, (iii) computational complexity that should be limited in order to ensure low latency, and (iv) reliability of the proposed techniques.

In this thesis, these drawbacks are discussed in detail and addressed by proposing a solution to achieve our goal, i.e. frailty early detection via wearable sensors. The main contributions of this work are:

• Exploration of the different parameters for a telemonitoring solution and selection of the needed tools while justifying our choice • Proposal of different methods for Human Activity Recognition (HAR)

• Validation of these methods on public datasets • Proposal of activity and health features to be extracted from localized data • Examination of the correlation between these features and the frailty status • Validation of the two previous steps in free-living conditions using data of communitydwelling elderly

Thesis Organization

To address all of the aforementioned issues, Chapter 1 introduces the problem statement by reviewing the medical context of frailty, and thus justifies the need of this project. Chapter 2 explores the components of a telemonitoring system in terms of system hardware and software implementation. This review gives an idea about the most suitable components for a low-cost and accurate system. Moreover, it describes the design of two datasets created by our team, namely FallAllD and ActFreeLi. The former consists of simulated human falls and ADLs following a predefined protocol, and is used to develop and validate our machine learning-based techniques for activity recognition. The latter consists of elder's activities in free-living conditions without any instructions, and is used to evaluate frailty conditions of elderly via wearable sensors. Chapter 3 presents some approaches to recognize and localize the targeted ADLs, and illustrates the experimental results on FallAllD and other public datasets. Chapter 4 displays the proposed activity and health features to associate them with frailty status. Now, their correlation with health conditions of elderly and their ability to detect physical weakening are validated on ActFreeLi dataset. Afterwards, the thesis is finally concluded and future work is suggested.

Chapter 1

BACKGROUND AND PROBLEM STATEMENT

This chapter introduces the geriatric syndrome called frailty in the medical context. First, we discuss frailty with its corresponding characteristics and outcomes. Then, we present some questionnaires and performance tests that have been developed to assess the well-being of elderly, as well as studies existing in the literature to detect and analyze frailty. Afterwards, since the risk of falling increases in frail older adults, fall detection is briefly reviewed. Finally, the limitations and drawbacks of the literature and related works are highlighted before listing the thesis objectives.

Frailty Syndrome

Frailty has been a trending topic in the past decades, and remains an emerging clinical and public health priority [START_REF] Clegg | Frailty in elderly people[END_REF][START_REF] Fried | Untangling the concepts of disability, frailty, and comorbidity: implications for improved targeting and care[END_REF][START_REF] Lang | Frailty: learnings from the safes cohort study and future perspectives for the research[END_REF][START_REF] Morley | A simple frailty questionnaire (frail) predicts outcomes in middle aged african americans[END_REF]Thibaud et al., 2021). Even though its definition is controversial [START_REF] Fisher | Just what defines frailty?[END_REF], frailty is conceptualized as a clinical syndrome symbolized by reduced resistance to stressors, resulting from age-associated cumulative declines in physiological function across multiple organ systems [START_REF] Fried | From bedside to bench: research agenda for frailty[END_REF][START_REF] Hoogendijk | Frailty: implications for clinical practice and public health[END_REF][START_REF] Lipsitz | Dynamics of stability: the physiologic basis of functional health and frailty[END_REF]. It is identified by functional weakening and sarcopenia, i.e. loss of muscle tissue, and causes adverse health outcomes. Frailty has been historically given a wide range of meanings [START_REF] Fried | Frailty[END_REF]. It is worth mentioning that frailty is neither synonymous with comorbidity nor disability. Comorbidity is an etiologic risk factor for frailty, while disability is one of its outcomes. hardly reversible. This potential reversibility is one of the major points justifying the interest in the frailty syndrome, if detected and treated early enough (Inserm, 2015;[START_REF] Marcucci | Interventions to prevent, delay or reverse frailty in older people: a journey towards clinical guidelines[END_REF]Travers et al., 2019). It was demonstrated that frailty increases the risk of falls, lack of autonomy, and hospitalization [START_REF] Rockwood | Frailty in relation to the accumulation of deficits[END_REF]Strandberg and Pitkälä, 2007).

Moreover, it is a strong predictor of 1-year and 5-year mortality [START_REF] Mudge | Frailty: mind the gap[END_REF], while being independently associated with increased ICU and 6-month mortality [START_REF] Maguet | Prevalence and impact of frailty on mortality in elderly icu patients: a prospective, multicenter, observational study[END_REF].

Frailty is being quantified using different approaches. On the one hand, the Frailty Index (FrI), proposed by Rockwood et al., is based on a comprehensive geriatric evaluation by counting the accumulated deficits, including cognitive and functional impairments, diseases, and psychosocial risk factors [START_REF] Mitnitski | Accumulation of deficits as a proxy measure of aging[END_REF][START_REF] Rockwood | A global clinical measure of fitness and frailty in elderly people[END_REF]. This is one of the commonly used ways to assess frailty. Despite its clinical usefulness in risk assessment, FrI presents a major drawback. Instead of discerning between frailty and disability/comorbidity, it includes their associated deficits, making it hard to inspect the underlying factor of this syndrome. On the other hand, a second widely-used approach was developed by Fried et al., defining frailty based on a specific phenotype [START_REF] Fried | Frailty in older adults: evidence for a phenotype[END_REF]. Figure 1.2.a illustrates the cycle of frailty.

The blue terms constitute its simplified version. In brief, the sarcopenia (1), which is caused by chronic undernutrition (8), changes in the musculoskeletal system (9), and/or various diseases [START_REF] Fried | Frailty in older adults: evidence for a phenotype[END_REF][START_REF] Fried | Frailty[END_REF]: (a) its simplified version in blue and (b) the frailty phenotype criteria.

1.1. Frailty Syndrome a) b) (2) (3) (4) (5) (6) (7) (8) (1) (9) (10) Figure 1.2 -Frailty cycle
(10), reduces the resting metabolic rate (2), the strength and the power of the patient (3) as well as the maximum volume of oxygen consumption (4). The two latter (i.e. ( 3) and ( 4)) reduce the walking speed (5) thus the person's activity ( 6). The resting metabolic rate (2) and the activity (6) lead to a decrease in the total energy expenditure (7), which could cause chronic undernutrition (8), thus closing the cycle. Hence, the Frailty Phenotype (FrP) characterizes frailty as a clinical syndrome meeting at least three out of five criteria (highlighted in Figure 1.2.b): (i) unintentional weight loss (10 lbs in past year), (ii) self-reported exhaustion (power), (iii) weakness (grip strength), (iv) slow walking speed and (v) low physical activity (through a questionnaire). Older adults with none of these five criteria are classified as non-frail, whereas elderly with one or two criteria are considered as pre-frail. FrP was tested in the Cardiovascular Health Study [START_REF] Fried | Frailty in older adults: evidence for a phenotype[END_REF]. It was observed that frailty increases with age and is greater in women than in men. Besides, intermediate frailty status (1 or 2 criteria) increased the risk of becoming frail over the next 3-4 years.

Identification and Assessment: Related Work

Researches and studies have been multiplied to find approaches and models with a view to frailty detection, analysis, and risk assessment, as well as physical function examination. First of all, some self-reported measures, self-evaluation questionnaires, and other performance tests have been proposed to evaluate the physical condition and the frailty status of older individuals.

The widely used approach is Fried's FrP [START_REF] Fried | Frailty in older adults: evidence for a phenotype[END_REF] previously discussed. The test begins by denoting the possible existence of unintentional weight loss (not due to exercise or dieting) of at least 5% of previous year weight and the self-reported exhaustion by asking two multiple choices questions. Next, the number of calories per week is calculated. It is stratified by gender and compared to a threshold, based on the short version of the Minnesota Leisure Time Activity questionnaire. Finally, the 15 feet walk time, which is stratified by gender and height, and the grip strength, which is stratified by gender and body mass index, are evaluated and compared to a threshold. The Clinical Frailty Scale (CFS) [START_REF] Mendiratta | Clinical frailty scale[END_REF] was also developed to stratify elderly (aged ≥ 65) into 9 different classes, from very fit to terminally ill. Furthermore, the Short Physical Performance Battery (SPPB) [START_REF] Guralnik | A short physical performance battery assessing lower extremity function: association with self-reported disability and prediction of mortality and nursing home admission[END_REF], which is a mixture of three tests, was proposed to evaluate the muscle strength, balance, and mobility.

Those tests are (i) balance test, where the patient must be able to stand on his own for 10 seconds following side-by-side, semi-tandem, and tandem position (see Figure A.1), (ii) 4-meter gait speed test, and (iii) chair stand test, where the subject must sit on the chair then stand up for five consecutive times. Additionally, Pittsburgh Sleep Quality Index (PSQI) [START_REF] Buysse | The pittsburgh sleep quality index: a new instrument for psychiatric practice and research[END_REF]) is a questionnaire that was designed to measure the quality of sleep. The PSQI includes a score for calculating a patient's seven sub-scores, each of which can range from 0 to 3. The [START_REF] Ferrucci | The origins of age-related proinflammatory state[END_REF], have not been shown to be reliable predictors of transitions from robust to pre-frail then frail [START_REF] Puts | Endocrine and inflammatory markers as predictors of frailty[END_REF][START_REF] Reiner | Inflammation and thrombosis biomarkers and incident frailty in postmenopausal women[END_REF]. Metabolic markers, particularly Glycated hemoglobin HbA 1C (a simple laboratory test), have been also subject to several studies. Very low HbA 1C levels have been linked to increased falls and mortality risk in frail individuals (Abdelhafiz and Sinclair, 2015; [START_REF] Nelson | The relationship between glycemic control and falls in older adults[END_REF]. Nevertheless, its capacity to detect the transition between the three frailty classes is yet to be proven. Meanwhile, hormonal changes, such as Vitamin D and testosterone, occur as the human body ages, leading to physiological impairment. Although Vitamin D deficiency has been associated with increased rates of frailty (Alvarez-Ríís et al., 2015;[START_REF] Hirani | Associations between frailty and serum 25-hydroxyvitamin d and 1,25-dihydroxyvitamin d concentrations in older australian men: the concord health and ageing in men project[END_REF], its quantification into a specific diagnostic metric is challenging and complicated due to its highly variable normal range among seasons, racial groups, and geographical regions. Moreover, there are some doubts on testosterone being used as a screening tool for frailty, seeing that a small amount of evidence exists to suggest a correlation between this hormonal change and the frailty trajectory [START_REF] Carcaillon | Sex differences in the association between serum levels of testosterone and frailty in an elderly population: the toledo study for healthy aging[END_REF][START_REF] Hyde | Low free testosterone predicts frailty in older men: the health in men study[END_REF].

Furthermore, statistical studies and data science were considered to extract knowledge and insights from collected data in order to examine the correlation/relationship between physical weakness and wellbeing/frailty status. The sedentary behavior and physical activity level, which were assessed using the International Questionnaire of Physical Activity, have been linked to frailty in elderly, using chi-square and Poisson regression tests with a statistical significance of 5% [START_REF] Da Silva | Association between frailty and the combination of physical activity level and sedentary behavior in older adults[END_REF]. By the same token, hourly activity data from wrist accelerometry measurement were analyzed to determine the relation between frailty and activity among older adults, using mixed-effects linear regression, to model the logarithm of hourly counts per minute [START_REF] Huisingh-Scheetz | The Relationship Between Physical Activity and Frailty Among U.S. Older Adults Based on Hourly Accelerometry Data[END_REF]. Moreover, two predictive models were proposed, namely frailty risk model and worsening risk model, by exploiting socioclinical databases [START_REF] Bertini | Predicting frailty condition in elderly using multidimensional socioclinical databases[END_REF].

The former stratifies subjects older than 65 years old into five classes (non-frail, pre-frail 1, prefrail 2, pre-frail 3, frail), using personal, health, and social data as inputs for logistic regression.

The latter further classifies each subject, identified as non-frail by the first model, into two classes according to risk of becoming frail within the year ("not-at-risk" and "at-risk"). A classification tree was also designed to assist inexperienced raters in decision-making and routine scoring of the CFS (Theou et al., 2021). It has been shown that the CFS classification tree rating, which is developed to ensure comprehensive geriatric assessment, was close enough to the expert geriatrician ratings in 93% of the time. Meanwhile, another study suggests that daily patterns of accelerometer activity are good indicators to predict changes in sleep, cognition, and mortality of older men, particularly worsening of sleep, changes in cognition, and shorter survival [START_REF] Zeitzer | Daily patterns of accelerometer activity predict changes in sleep, cognition, and mortality in older men[END_REF]. Functional principal component analysis was used to inspect the aforementioned patterns over the course of 4-7 days. Likewise, frailty and time-varying comorbidities were revealed as important parameters for clinical decision making, by using temporal features and non-temporal data which feed a Deep Neural Network (DNN) to predict death within one year [START_REF] Shah | Frailty and cardiovascular surgery, deep neural network versus support vector machine to predict death[END_REF]. More importantly, the gait speed, measured over short distances and compared to thresholds, has been a trending topic in the past two decades. It was described as one of the strongest predictors of incident disability [START_REF] Perera | Gait speed predicts incident disability: a pooled analysis[END_REF], as well as health-related outcomes of well-being [START_REF] Cesari | Prognostic value of usual gait speed in wellfunctioning older people-results from the health, aging and body composition study[END_REF]. Other studies have suggested the walking speed as a robust measure for physical function monitoring, and provided several recommendations on procedures to evaluate this variable, like the optimal distance, the experimental protocol, and so on [START_REF] Middleton | Walking speed: the functional vital sign[END_REF]. Moreover, this variable was linked to survival in older adults (Studenski et al., 2011). Some other gait parameters were also discussed in the literature. Kressig et al. proposed a set of temporal and spatial features like cadence, stride length, stance, etc. to better understand the effect of frailty on the movements [START_REF] Kressig | Temporal and spatial features of gait in older adults transitioning to frailty[END_REF]. The gait variability was also targeted and associated with frailty in elderly [START_REF] Montero-Odasso | Gait variability is associated with frailty in community-dwelling older adults[END_REF]. Additional variables like displacement and smoothness of the center of pressure trace were inspected [START_REF] Hass | Gait initiation in older adults with postural instability[END_REF].

More recently, some works conducted observational studies by monitoring a set of different activity metrics from wearable sensors in relation to frailty status and health conditions. A pendant sensor was employed to monitor the physical activity of elderly (≥ 60 years old) over 48 hours, by observing the body posture (walking, sitting, standing), the activity behavior (sedentary, light, moderate-to-vigorous), steps parameters, and sleep parameters [START_REF] Razjouyan | Wearable sensors and the assessment of frailty among vulnerable older adults: an observational cohort study[END_REF]. The first three parameters were statistically correlated with the different frailty 54 1.3. Fall Detection stages, and their mixture achieved an Area Under Curve (AUC) of 0.88 for identifying prefrail elderly. However, sleep parameters were not able to classify older adults into three frailty statuses. This study was further extended to assess cognitive frailty in community-dwelling older people [START_REF] Razjouyan | Toward using wearables to remotely monitor cognitive frailty in community-living older adults: an observational study[END_REF]. The goal was to recognize the presence of both (i) physical frailty (defined by FrP) and (ii) cognitive impairment (defined by the score of Mini-Mental State Examination) using a chest-worn sensor over 48 hours. The considered features, namely sleep parameters, physical activity behavior, percentage of walk, and step counts, were shown to be statistically significant for this application (p < 0.05). A decision tree classifier reached an AUC of 0.75. Another research has taken place to evaluate the reliability of wearable devices for assessing frailty in older home care clients [START_REF] Kim | Consumer-grade wearable device for predicting frailty in canadian home care service clients: prospective observational proof-of-concept study[END_REF]. Acquired data of participants aged 55 years and older were exploited to derive variables including daily step count, sleep time and quality, and heart rate over a period of 9.43 (± 1.99) days. It was demonstrated that frail seniors walked less and slept longer. A logistic regression model fitted with number of steps, age, education level, and deep sleep time was able to distinguish frail people from non-frail with an AUC of 0.9. Besides, gait parameters, such as gait speed, stride time, swing/stance phase, cadence (steps per minute), Timed Up and Go (TUG) test (in s), the score of Dynamic Gait Index (DGI), and the double support time (in ms), were inspected to see their ability to separate frailty levels (Apsega et al., 2020). Those parameters were calculated under supervised conditions, where participants walked a distance of 4 m at the self-selected usual pace, using wireless sensors fixed on the lower limb segments. Stride time, stance phase, and cadence were shown to be the most sensitive parameters to discriminate populations in pairs, i.e. separate frail or pre-frail individuals from robust, using multinomial logistic regression models and statistical significance (p values).

Fall Detection

As previously discussed, frailty is one of the main risk factors for falling in elderly [START_REF] Clegg | Frailty in elderly people[END_REF][START_REF] Fried | Frailty in older adults: evidence for a phenotype[END_REF][START_REF] Hoogendijk | Frailty: implications for clinical practice and public health[END_REF][START_REF] Rockwood | Frailty in relation to the accumulation of deficits[END_REF]. A fall is an abnormal incident that is very dangerous on the human body. Falls can be fatal for elderly, leading to traumatic brain injury, hospital admissions, disability, and even death [START_REF] Botek | Why are falls so dangerous for the elderly? Aging Care[END_REF].

Recent statistics show that, each year, more than 37 million falls necessitate medical attention [START_REF] Who | Falls[END_REF]. Consequently, it is necessary to identify falls to avoid health implications on the individual. To cope with this issue, automatic fall detection systems were developed, ensuring timely medical intervention. Fall detection has been heavily targeted over the past decades [START_REF] Charlon | Design and evaluation of a device worn for fall detection and localization: application for the continuous monitoring of risks incurred by dependents in an alzheimer's care unit[END_REF]Tamura et al., 2009;Thome et al., 2008), and is still an active research area [START_REF] Saleh | Elderly fall detection using wearable sensors: a low cost highly accurate algorithm[END_REF]G. Wang et al., 2020;[START_REF] Zhong | Multi-occupancy fall detection using non-invasive thermal vision sensor[END_REF]. Figure 1.4 illustrates the different phases of a human fall over twelve seconds. The subject fell forward while walking due to a slip. He remained on the floor after the shock. The pre-fall phase consists of random gestures, which are not related to the fall. In this case, this phase contains the movements of the subject while walking. Afterwards, the pre-impact phase (where the human body is on the verge of hitting the floor) and the impact phase (containing the shock/peak) occur. The latter is followed by a certain adjustment, where the human is moving to his final position, before staying still (inactivity phase). The critical phase is about 2 s and is centered on the peak (shock), whereas both the adjustment and the inactivity phase constitute the postimpact phase. It is worth mentioning that fall detection could be a complicated task, since the successive movements of certain ADLs, like lying heavily on the bed, resemble those of falling. Hence, intelligent algorithms must be implemented to avoid generating false alarms.

Nonetheless, an older individual might be able to recover after falling. However, unfavorable outcomes could still emerge later even if the older person is not in pain and is unaware of potential damage. For instance, subdural hematoma may occur due to a minor trauma, especially if this person consumes medications and/or blood thinners [START_REF] Saleh | Fallalld: an open dataset of human falls and activities of daily living for classical and deep learning applications[END_REF]Tanaka and Ohno, 2013). Indeed, the consideration of falls with recovery, while developing fall detection systems, is recommended in the literature [START_REF] Noury | A proposal for the classification and evaluation of fall detectors[END_REF].

Fall detectors are divided into ambient/external sensors (like cameras) and wearable sensors.

The goal is to automatically detect the fall in order to inform authorized teams and/or family tion by developing a system which generates alarms and sends them via a Bluetooth module [START_REF] Pierleoni | A wearable fall detector for elderly people based on ahrs and barometric sensor[END_REF]. A mobile application was developed to make prerecorded phone calls after receiving alarms from the sensor node. He et al. created an alerting system which distinguishes falls from ADLs (J. [START_REF] He | An unobtrusive fall detection and alerting system based on kalman filter and bayes network classifier[END_REF]. As soon as the system detects a fall, an alarm is sent to caregivers to provide timely and accurate help for the elderly. Tamura et al. produced a wearable airbag incorporating a fall-detection system (Tamura et al., 2009). The algorithm they developed detects the pre-impact phase (300 ms before the fall incident). A signal triggers the inflation of the airbag, reducing serious outcomes and injuries caused by fatal falls. Note that, in addition to the emergency alerts, the geographical position of the elderly must be sent.

Therefore, indoor/outdoor positioning is also a priority for health management, particularly for elderly care. In this case, vulnerable subjects who regularly fall are found in a timely manner.

These techniques are based on technologies such as Infrared Ray, RFID, Wifi/WLAN, GPS, to name a few.

Limitations and Drawbacks

Despite the aforementioned efforts and approaches to detect and analyze the frailty syndrome in older adults, there are still a number of limitations and drawbacks which should be mentioned.

On the one hand, both FrP and FrI criteria determine the pre-frailty and frailty statuses in clinical settings at a particular moment. Nevertheless, their effectiveness is limited when it comes to the prediction and identification of the progression from robust/pre-frail to frail. They are also sensitive to the conditions (like the emotional state of the subject for instance) under which they were done. Furthermore, the capability of questionnaires and performance tests (like PSQI and SPPB) to monitor and recognize the frailty trajectory is questionable. Firstly, these approaches are based on some subjective measurements. While this kind of data is helpful and important in well-being assessment, it is not sufficient to define a full and accurate tracking system. Secondly, the measures are done in supervised conditions, i.e. the subject has to complete these questionnaires/tests with the assistance of a practitioner, which is in contradiction with the notion of prevention. Finally, these tests provide short-term estimation of physical capacities at a single point in time.

On the other hand, it was seen that there is a lack of robust biomarkers for frailty detection and worsening risk prediction. Despite being clinically plausible diagnostic tools, these markers and hormonal changes might fail to stratify elderly into different frailty states, i.e. discriminate frail/pre-frail from robust elderly people. Therefore, their relationships to the syndrome are not clear. Additionally, further research is required to identify their ability to predict the transition from one frailty stage to another. This justifies why practical and reliable approaches and as-sessments are still missing and alternative procedures are needed. Besides, fall detection does not resolve the problem either. It is a good strategy to ensure timely intervention and provide medical care. However, the older person could endure serious injuries like broken hip or pelvic fracture even after medical aid, which lead to lack of autonomy or disability. Moreover, falling frequently means that the subject is already vulnerable/frail. Hence, the goal should be a transition from curative systems to preventive systems, i.e. researchers should target fall prevention instead of fall detection, in order to avoid all these dramatic consequences and interrupt the progression towards frailty (and disability later).

Diversely, some attempts were made to analyze this syndrome via wearable sensors, by associating some parameters and/or activity metrics with frailty status, and by studying their correlations. Even though the importance of remote monitoring was demonstrated by these works, wider sets of variables are required, and researchers still need to consider which outcomes are mostly useful to quantify physical activity of elderly [START_REF] Mc Ardle | Quantifying physical activity in aged residential care facilities: a structured review[END_REF]. Additionally, frailty is a complicated syndrome which should be symbolized by an ensemble of heterogeneous parameters, thus the discrimination power of systems involving a combination of features should be evaluated instead of inspecting the correlation between the frailty status and one single metric.

To date, the most relevant/discriminant features are not known, and whether they are subjectdependent is still an open question. Apart from that, most experiments include relatively young volunteers (less than 65 years old) [START_REF] Kim | Consumer-grade wearable device for predicting frailty in canadian home care service clients: prospective observational proof-of-concept study[END_REF][START_REF] Razjouyan | Wearable sensors and the assessment of frailty among vulnerable older adults: an observational cohort study[END_REF] and are based on clinical trials with a predefined protocol (Apsega et al., 2020;[START_REF] Carneiro | Accelerometerbased methods for energy expenditure using the smartphone[END_REF]. Even in freeliving conditions, a short-term evaluation is usually considered [START_REF] Kim | Consumer-grade wearable device for predicting frailty in canadian home care service clients: prospective observational proof-of-concept study[END_REF][START_REF] Razjouyan | Wearable sensors and the assessment of frailty among vulnerable older adults: an observational cohort study[END_REF][START_REF] Razjouyan | Toward using wearables to remotely monitor cognitive frailty in community-living older adults: an observational study[END_REF][START_REF] Rosenberger | Twenty-four hours of sleep, sedentary behavior, and physical activity with nine wearable devices[END_REF] (such as 24-48 h or some few days).

The short-term monitoring and/or clinical trials may be insufficient to represent the overall activities of elderly in natural conditions, leading to biased results. Now, when it comes to human gait, other drawbacks can be denoted. Walking is a complex activity of daily routine and cannot be only restricted to the gait velocity, despite its great importance. Other parameters may vary during the transition towards frailty. Although some informative features (like the stance and swing phases, the stride time, and the cadence) were proposed, we still do not know much about the relationship between the gait parameters and the categorical frailty classes [START_REF] Schwenk | Frailty and technology: a systematic review of gait analysis in those with frailty[END_REF]. Figure 1.5 illustrates the cycle of human gait.

The stance phase starts from the moment the foot (black one in the figure) touches the ground to the moment the same foot leaves it. This phase constitutes around 60% of the gait cycle. The swing phase is somewhat the opposite, i.e. starts when the foot leaves the ground and ends when it touches the floor again, constituting the remaining 40% of the cycle. Both phases lead to the stride time (gait cycle). It can be seen that the use of those three variables, i.e. stance, swing, and stride is somewhat redundant, since they are related to each other in some way. Further analysis is needed to define a robust module which is able to predict the transition between frailty classes

Stance (60%)

Swing (40%)

Stride (gait cycle)

Figure 1.5 -The human gait cycle, with the corresponding stance and swing phases which constitute around 60% and 40% of the cycle respectively. This is a simplified version of the functional divisions of the gait cycle originally published in (Stöckel et al., 2015).

using a set of descriptive gait indicators [START_REF] Panhwar | Assessment of frailty: a survey of quantitative and clinical methods[END_REF], without being limited to the statistical significance of these basic and redundant parameters. There is a lack of predictive systems being able to extract features from acquired signals in unsupervised conditions, in order to assess the frailty trajectory of older adults and target preventive interventions. Moreover, the gait analysis has not been implemented in routine assessment of frailty status in older individuals [START_REF] Schwenk | Frailty and technology: a systematic review of gait analysis in those with frailty[END_REF].

Considering all the aforementioned points and remarks, frailty clearly remains an open research challenge and an active area to date. Even though this syndrome has been a trending topic in the past decades, some aspects still need to be clarified to propose innovative solutions for preventive systems. New studies coupled with experiments in real world conditions are required for a better understanding in order to avoid adverse outcomes and make people age healthily at home.

Thesis Objectives

This thesis mainly focuses on activity monitoring of elderly with a view to frailty analysis and prevention. The main goal is the creation of a fully automated system which is able to assess the physical function of older adults continuously in unsupervised conditions, leading to frailty early detection in order to interrupt the transition towards disability and lack of autonomy. Figure 1.6 illustrates the flow diagram of this work. The objective is to monitor the activity of elderly in order to send health reports to the medical team and the family members. A feedback (set of recommendations) is sent back to the elderly to close the cycle. In the remainder of this chapter,

Wearable Sensor-based Monitoring

The current work is based on wearable sensors for many reasons. Firstly, the measurements are objective and calculated from acquired data, unlike questionnaires FrP and FrI where some data are subjective and based on approximations. Secondly, in terms of privacy, wearable sensors do not reveal the subject's identity, thus have an advantage over ambient sensors. Thirdly, since they are body-worn, they supply data anywhere continuously. Even though external sensors outperform wearable ones in some applications, like the analysis of movement trajectories in living areas [START_REF] Campo | Behaviour monitoring of the elderly by trajectories analysis[END_REF], they are limited to certain environments and can only cover a certain detection zone. Fourthly, camera-based HAR has its limitations like diversity in camera views, variety in environmental conditions, and variety of human subjects (J. [START_REF] Liu | Ntu rgb+d 120: a large-scale benchmark for 3d human activity understanding[END_REF].

Activity Monitoring

Elderly

Health Reports

Feedback Data Acquisition

Activity Recognition Activity Analysis

Human Activity Recognition

Fully automated and unsupervised conditions are two keywords that require the implementation of a HAR module. Since data are acquired continuously in daily routine under free-living conditions, the pattern of the signals should be analyzed and artificial intelligence should be exploited in order to recognize the human gestures. Hence, reliable algorithms should be developed to segment these data using sliding windows and to predict the activity over each window using machine learning techniques. In this case, the ADLs are accurately localized, including the corresponding time of occurrence as well as the duration.

Physical Weakening Identification

The previous step, i.e. HAR module, is a tool to segment, recognize, and localize the ADLs automatically. Now, once detected and localized, these ADLs must be analyzed by extracting informative features which reveal the health status of elderly. These features can be divided into two main categories: (a) global features, computed over the course of the day, and (b) local features, computed over local segments of acquired data, i.e. related to a specific activity. The discrimination power of these features, their correlation with frailty trajectory, and their ability to detect progressive weakening, should be discussed and interpreted in detail using statistical tests and machine learning techniques. The goal here is to reveal the most relevant variables and measurements in this context, and to create a reliable preventive system for frailty early detection.

Evaluation using Different Experimental Settings

For HAR module, the performance evaluation should be done under supervised conditions using predefined experimental protocols. The goal here is to assess the system ability to detect the succession of movements following different scenarios. The subject is first instructed to make a set of gestures while wearing the device. Afterwards, acquired data constitute the input of the HAR module to see whether we are able to recognize the simulated activities. Therefore, a dataset of human ADLs should be developed. Several subjects have to be recruited, in order to build this dataset. The participants will wear the device while simulating a set of activities.

More details are given in section 2.4.1.

For frailty analysis module, the case is different. Here, the capacity to detect frailty should be done in free-living conditions, under unsupervised conditions. Hence, the performance is meaningful since the metrics and features are calculated while the subject is acting freely, contrarily to most state-of-the-art studies (as seen in the previous section) where he is instructed to perform a set of movements in a specified way. For example, an optimal measurement of gait velocity is computed when the elderly attempts to walk on his own during his daily routine. The same remark holds for other ADLs. Hence, older adults of diverse profiles have to be recruited. The goal now is to let the participants wear the sensing device during their daily routine, and act freely without any specific instruction being imposed. More details are given in section 2.4.2.

In conclusion, frailty is a clinical syndrome leading to physiological impairment and unfavorable health outcomes such as increased falls, lack of autonomy, hospitalization, and death.

It might be reversible or attenuated by medical interventions, hence the need for preventive systems. This chapter described this illness from a medical point of view. Several attempts have been made to detect this illness and cope with its issues. Nonetheless, it was seen that several limitations and major drawbacks exist when it comes to state-of-the-art works and studies. As life expectancy is increasing worldwide, the prevalence and clinical outcomes of frailty syndrome will expand rapidly. Consequently, we can see a growing necessity to concentrate on research directed towards finding novel, viable, and efficient approaches and strategies to take on the challenge of frailty prevention, an actual world health organization priority. The present work aims at developing a wearable sensor-based telemonitoring system with a view to frailty analysis.

The physical function being linked to this syndrome (unlike biomarkers and hormonal changes for example), we propose an approach ensuring continuous activity surveillance for frailty early detection. Our goal is to find the most relevant indicators for progressive physical weakening detection, using data of community-dwelling elderly in free-living and real world conditions. In the next chapter, we explore the constituents and tools of telemonitoring solutions in terms of employed sensors (number of sensors and the nature of acquired signals), their body placement, and their characteristics such as power consumption, resolution, sampling frequency, and potential artifacts, in order to develop a sensing unit responding to our requests and needs.

Chapter 2

CHOICE OF THE TELEMONITORING SOLUTION

This chapter discusses the tools to develop a wearable sensor-based telemonitoring solution in terms of hardware and software. In general, the recognition process consists of two main parts:

(a) a low-level acquisition unit that continuously collects data, (b) a signal/image processing and feature extraction module whose output feeds a classifier to label the recorded signals. This chapter starts by introducing the different types of sensors which may be used in a recognition system as well as their characteristics. Afterwards, the effect of the body placement on the acquisition and on the reliability of the system is highlighted. Besides, a brief discussion on processing units and software implementation is proposed before describing the design of two datasets, which were created to serve and evaluate both the HAR and frailty analysis modules.

Sensors

Miniaturized wearable sensors are auspicious tools for any gesture recognition system. The design and development of small, light-weight and low-cost smart sensors are usually taken into consideration for acceptability purposes. The widely used sensor is the tri-axial accelerometer. This sensor measures the acceleration, which is the basis of most, if not all, monitoring approaches.

Generally, two types of accelerometers are deployed in wearable trackers, namely (a) Micro-Electro-Mechanical Systems (MEMS) and (b) PiezoElectriC (PEC). The former is composed of micro components made of silicon, polymers, metals and/or ceramics (How To Mechatronics, 2016). When an acceleration a is applied, the mass moves and a change in capacitance occurs, resulting in a particular acceleration value. Now, certain crystals (PEC material) have the property of generating a voltage when subjected to pressure. When a physical force F is exerted, the seismic mass m loads the PEC element [START_REF] Wagner | Piezoelectric accelerometers theory and application[END_REF] according to Newton's second law of motion: F = m a. The force exerted is observed by the change in the electrostatic voltage (generated by the PEC material). Seeing that PEC accelerometers possess low output analog signal, there is a need for amplification in addition to an analog to digital converter. Table 2.1 summarizes the advantages of one type over the other (Albarbar and Teay, 2017;[START_REF] Di Pietro | Capacitive mems accelerometer for condition monitoring[END_REF]TE Connectivity, 2017;[START_REF] Vectornav | Accelerometer[END_REF][START_REF] Wagner | Piezoelectric accelerometers theory and application[END_REF]. It is [START_REF] Vectornav | Accelerometer[END_REF]. Diversely, PEC ones operate in very high temperatures (up to 350 • C) and handle very high impact shock (> 200 g units). Moreover, they possess very high frequency range (> 500 Hz). However, the aforementioned advantages do not offer much in this context, seeing that the goal is human gesture recognition. The human body cannot endure such high temperatures, nor such very high impact shocks. Moreover, the aforementioned frequency range is not interesting in our case, since the range of human body motion is up to 20 Hz [START_REF] Bouten | A triaxial accelerometer and portable data processing unit for the assessment of daily physical activity[END_REF]. Based on the aforementioned remarks, MEMS were retained in our work.

The second widely used sensor is the tri-axial gyroscope. This sensor, with an electrically powered motor and metal gimbals, is able to measure orientation and angular velocity. Coupled with an accelerometer, they both constitute an Inertial Measurement Unit (IMU), which is able to monitor translational and rotational motions. The angular velocity is an added-value to any recognition system. Nevertheless, gyroscopes require very high power consumption compared to accelerometers (Q. [START_REF] Liu | Gazelle: energy-efficient wearable analysis for running[END_REF]. Figure 2.1 illustrates the average current consumed with respect to the sampling frequency. As a matter of fact, the average current consumed by the gyroscope could be ten to a hundred times greater than that consumed by the accelerometer for the same sampling frequency. This could be a major drawback for wearable devices, since the battery life of these devices is a critical point for acceptability. Elderly could end up refusing a device that often needs to be recharged or the battery replaced. The target is usually to reduce the power consumption, so small batteries can be deployed, thus creating the opportunity for producing light-weight trackers.

The tri-axial magnetometer is a third well-known sensor, which is also employed in a widerange of monitoring systems. This device measures magnetic field or magnetic dipole moment, particularly the Earth's magnetic field. Consequently, by adding the magnetometer to an IMU, Therefore, the usage of magnetometer may not always be an added-value to an activity tracker.

Finally, the barometer is another sensor which could be employed in an inertial system. This instrument measures atmospheric pressure in a certain environment, as well as the temperature.

While the first three sensors are used to track the movement of the wearable sensing unit in a three-dimensional space, the barometer is used as a complementary part to estimate the altitude of the device. The atmospheric pressure and the altitude are inversely proportional.

Based on the previous descriptions, we conclude that an inertial system is usually either (i) a 3-DoF system, i.e. based on a tri-axial accelerometer, (ii) a 6-DoF system, i.e. based on an IMU (tri-axial accelerometer + tri-axial gyroscope), or (iii) a 9-DoF system, i.e. a MARG sensing unit (IMU + tri-axial magnetometer). Note that by adding an on-board processing system to an IMU or a MARG sensor, i.e. by employing a sensor fusion technique, we create an Attitude and Heading Reference System (AHRS), which provides attitude and heading information, or in other words the orientation estimation of the device in a 3D space (Earth frame). This part will be discussed in the next sections. Now, seeing the large power consumption of gyroscopes, and the anomaly related to magnetometers in indoor environments, acceleration-based solutions may be preferred, particularly using a MEMS accelerometer. In this case, the battery life is not drastically affected, hence the design of small, light-weight and low-cost smart sensors with a decent reliability is conceivable. Nonetheless, we might lose informative features by excluding the angular velocity and the magnetic fields, thus decrease the accuracy of the monitoring system.

The trade-off between power consumption and accuracy is an important factor when developing any tracking system. Additionally, a barometer can be added to one of the three inertial systems to estimate the altitude of the wearable device, which is an added value to a broad range of applications.

Sensor Placement

Several locations have been considered in the literature, when it comes to gesture recognition via wearable sensors, such as waist, chest, lower back, wrist, thigh, ankle to name a few [START_REF] Bonomi | Detection of type, duration, and intensity of physical activity using an accelerometer[END_REF][START_REF] Gjoreski | Accelerometer placement for posture recognition and fall detection[END_REF][START_REF] Parkka | Activity classification using realistic data from wearable sensors[END_REF][START_REF] Yeoh | Ambulatory monitoring of human posture and walking speed using wearable accelerometer sensors[END_REF]. Moreover, some HAR approaches employ multi-positional body sensors [START_REF] Bharti | Human: complex activity recognition with multi-modal multi-positional body sensing[END_REF][START_REF] Shoaib | Complex human activity recognition using smartphone and wrist-worn motion sensors[END_REF]. Whilst data fusion from different sources supplies sufficient interpretive information for an accurate recognition, wearing numerous sensors is burdensome for the user. Note that, in this work, as also recommended within the framework of the ACCORDS project, HAR was considered using one single wearable device.

The sensor placement is an important factor which affects the implementation of HAR techniques, as well as their reliability and accuracy. It is worth mentioning that acceleration signals, in general, increase in magnitude from head to ankle [START_REF] Mathie | Accelerometry: providing an integrated, practical method for long-term, ambulatory monitoring of human movement[END_REF]. Figure 2.2 illustrates acquired acceleration signals from six different positions, namely chest, lower back, hip, wrist, thigh, and foot, and we can observe that the magnitude is increasing from chest towards foot.

Hence, thigh-worn and ankle-worn sensors are highly sensitive to the human motion, i.e. high peaks may appear even when low to moderate intensity movements occur. This phenomenon might lead to an over-estimation of some acceleration-based parameters, thus biased results may be reported. Likewise, wrist-worn devices might generate signals of random shape that could mislead the processing units and thus increase the misclassification rate, since the arm is not fixed and moves in different directions even when performing the same activity. For instance, walking with a stroller, walking while folding arms, walking while holding a baby, and walking with free hands, are four different scenarios for the same activity (walking). However, a wrist-worn sensor will generate four different patterns for each scenario, which will decrease the accuracy of the recognition system. It is clear from Figure 2.2 that the shape of the acceleration signals acquired by the wrist-worn device are somewhat noisy compared to signals acquired from the chest, lower-back, and the hip/waist. Furthermore, since the arm moves with higher DoFs, some complex and/or unexpected movements could be performed. the elderly particularly appreciate wrist-worn trackers in general over other devices like clip-on for example [START_REF] Mercer | Acceptance of commercially available wearable activity trackers among adults aged over 50 and with chronic illness: a mixed-methods evaluation[END_REF][START_REF] Puri | User acceptance of wristworn activity trackers among community-dwelling older adults: mixed method study[END_REF], we will also consider this position when studying the recognition of ADLs (see Chapter 3 for details).

Processing Units and Modules

Preprocessing

Before extracting knowledge and calculating features to identify the physical activity, data must be preprocessed first. Raw data are integers. The acceleration values are first multiplied by a constant C A to convert them into g units (float numbers), the angular velocity values by C G to convert them into • /s, and the magnetic field values by C M to transform them into Gauss. These constants are equal to 2ρ/2 γ , where ρ is the sensor measurement range and γ is its resolution.

Moreover, the temperature T and the temperature compensated pressure P are calculated as follows:

                       dT = D 2 -C 5 × 2 8 T = 0.01 2000 + dT ×C 6 2 23 of f = C 2 × 2 16 + C 4 ×dT 2 7 sens = C 1 × 2 15 + C 3 ×dT 2 8 → P 0 = D 1 ×sens 2 21 P = 0.01 × P 0 -of f 2 15
(2.1) C 1 , ..., C 6 are the calibration coefficients (16 bits). They are specific to the barometer, and have been calculated by the manufacturer after calibration. D 1 and D 2 are digital data (24 bits) acquired by the barometer. Afterwards, the noisy pressure signal P is subject to a slope-limit filter (D. [START_REF] Chen | A wireless real-time fall detecting system based on barometer and accelerometer[END_REF][START_REF] Jatesiktat | An elderly fall detection using a wrist-worn accelerometer and barometer[END_REF]. This filter removes sudden peaks (the value of outliers) occurring in these signals, while keeping the shape of the transition if it exists.

In other words, it reduces the Standard Deviation (SD) of the signal while keeping its slope. The instructions shown in Algorithm 1 are done to obtain the slope-limited pressure signal P . The Algorithm 1 Slope-limit Filter for Barometric Pressure Signals 1: Define: δ (slope-limit) 2: Input: P (raw data) 3: Input: P (filtered pressure) 4: while true do 5:

Read new data-point P i 6:

if P i > P i-1 + δ then 7:

P i = P i-1 + δ 8:
else if P i < P i-1 -δ then 9:

P i = P i-1 -δ 10:
else 11: P i = P i slope-limit filter could be subject to another filter, namely the moving average filter (with n, the number of points inside the window, being odd). This filter smoothes the signal and reduces the noise even further. The output P of this filter is calculated as follows:

P i = 1 n (n-1)/2 j=-(n-1)/2 P i+j (2.2)
Figure 2.4 illustrates the raw barometric pressure signal, the slope-limited signal, and the output of the moving average filter. It is clear that the SD of the signal decreases after being subject to a slope-limit filter while keeping its slope (the pressure is increasing). The moving average filter, whose input is P (orange) and output is P (blue), smoothes the signal.

Finally, the acceleration magnitude ||a|| is an important component when it comes to HAR.

The preprocessing unit calculates ||a|| using the three acceleration components {a X , a Y , a Z } as follows:

||a|| = a 2 X + a 2 Y + a 2 Z (2.3)
Besides, the altitude H and the pressure P are inversely proportional. H is calculated as follows [START_REF] Intersema | Using ms5534 for altimeters and barometers[END_REF]: (2.4) where H is in meter, T in kelvin, and P in mbar. Note that P can be replaced by P or P for a robust altitude estimation.

H = T 0.0065 × 1 - P 1013.25 0.19

Attitude Estimation

To represent the 3D orientation of a body in regard to a fixed coordinate system, the Euler angles are generally considered. Those angles are denoted by ψ, θ, and φ. Figure 2.5 illustrates the orientation of a wearable sensor frame (D) relative to Earth frame (E) in terms of Euler angles. An AHRS provides the attitude (orientation) and heading information as previously mentioned. In the literature, the notion of gimbals has been introduced in mathematics to measure these angles. A gimbal is a ring which rotates around an axis. Hence, three gimbals are nested one within another to ensure 3D rotations. Therefore, the orientation is described as three axial rotations with Euler angles, i.e. applying a fixed set of successive rotations (each rotation around a specific axis). This operation can cause an issue called Gimbal lock. This phenomenon occurs in certain situations, where two gimbals line up (the axes of two gimbals become parallel). This leads to the loss of one DoF, and additional rotations from this point might lead to unexpected outcomes. A solution to this problem is the use of quaternions representation as described in Appendix B. Now, to estimate the orientation of the device, i.e. the Euler angles, an orientation filter is needed to process data and compute these angles. In the literature, the Kalman filter has become the cornerstone for the greater part of orientation systems [START_REF] Foxlin | Inertial head-tracker sensor fusion by a complementary separate-bias kalman filter[END_REF][START_REF] Marins | An extended kalman filter for quaternion-based orientation estimation using marg sensors[END_REF][START_REF] Sabatini | Quaternion-based extended kalman filter for determining orientation by inertial and magnetic sensing[END_REF]. Now, despite their high accuracy, the complex implementation and high This algorithm can be summarized in three steps. In the first step, data are read from the MARG sensor. Then, the gradient descent algorithm is applied to compute orientation increment (gradient step) using acceleration data, and magnetometer data for magnetic distortion compensation.

The direction of the gyroscope measurement error is then computed using numerical integration. The two aforementioned operations constitute the second step. Both measurements (from the second step) are fused in a third step to estimate the attitude. This algorithm can also be applied to an IMU, by excluding magnetic distortion compensation. Note that, conventionally, the direction of gravity ĝE defines the vertical z-axis (Eq. (2.5)), and the earth magnetic field bE is considered to have components following the horizontal x-axis and the vertical z-axis (Eq.

(2.6)) [START_REF] Madgwick | An efficient orientation filter for inertial and inertial / magnetic sensor arrays[END_REF]:

ĝE = [0 0 0 1] (2.5) bE = [0 b x 0 b z ] (2.6)
The aforementioned orientation filters, namely Extended Kalman Filter (EKF), Mahony, Madgwick, AQUA, and Fourati, were implemented using Python 3.6. The scripts were executed on an Intel(R) Xeon(R) Gold 5118 2.3-GHz processor with 64 GB RAM, to estimate quaternions of a human fall over 20 s. The execution time was measured in seconds. Table 2.2 illustrates the results. Madgwick's filter has the fastest response, with an execution time equal to 0.17 s.

This filter outperforms all the others in terms of complexity, including AQUA and Mahony. As expected, the Kalman filter requires high computational load, hence long execution time (1.03 s in this case). The same remark holds for Fourati's filter, which has a faster response but still considerably slow compared to Madgwick's filter.

Feature Extraction and Classification Process

The majority of HAR modules are based on machine learning techniques (Z. [START_REF] Wang | A review of wearable technologies for elderly care that can accurately track indoor position, recognize physical activities and monitor vital signs in real time[END_REF].

Here, two paths can be followed are done using two separate units.

Design of Datasets

Data are needed when developing machine learning-based approaches (in order to train classifiers and evaluate their performance) and to conduct reliable statistical studies. To achieve an acceptable reliability, we need a representative and realistic dataset containing a wide range of ADLs. To obtain a representative dataset, the shape of the acquired signals should clearly represent the movements of the subject. In other words, the sampling frequency F s and the measurement range m R are important factors when it comes to data acquisition. Some datasets used very low sampling frequencies (below 20 Hz) [START_REF] Wertner | An open labelled dataset for mobile phone sensing based fall detection[END_REF], while others selected low measurement ranges (±2 g) [START_REF] Micucci | Unimib shar: a dataset for human activity recognition using acceleration data from smartphones[END_REF][START_REF] Vavoulas | The mobifall dataset: an initial evaluation of fall detection algorithms using smartphones[END_REF]. A very low sampling frequency abolishes the possibility of calculating informative local features from signals,

especially that the range of human motion is up to 20 Hz as previously discussed. Moreover, most of acceleration signals are saturated even for common ADLs, especially when using MEMS accelerometers, which measure the static acceleration (Earth gravity of 1 g) and dynamic acceleration. Therefore, such datasets are not suitable for our task. Besides, some other public datasets can be found. UMAFall is a dataset consisting of human falls and ADLs [START_REF] Casilari | Umafall: a multisensor dataset for the research on automatic fall detection[END_REF] collected using an accelerometer, a gyroscope, and a magnetometer. Data were acquired with a waist-worn device consisting of three sensors (2 accelerometers and 1 gyroscope) at a sampling frequency of 200 Hz. Finally, mHealth is a public dataset comprising a set of body postures and recurrent ADLs [START_REF] Banos | Mhealthdroid: a novel framework for agile development of mobile health applications[END_REF][START_REF] Banos | Design, implementation and validation of a novel open framework for agile development of mobile health applications[END_REF]. Here, data were acquired using a tri-axial accelerometer attached to the chest with 2-lead ECG measurements, a wrist-worn MARG sensor, and an ankle-worn MARG sensor. Nonetheless, this dataset does not contain transient ADLs, which is a clear drawback to any recognition system.

Accordingly, we built two different datasets, which serve the two main objectives of this work. The first one is dedicated to HAR, and is called FallAllD (detailed in section 2.4.1). A set of human falls and ADLs were simulated by participants of diverse profiles under supervised conditions and following a predefined protocol. Acquired data were then segmented and labeled.

These data are used to train and test machine learning-based HAR algorithms. The second one is dedicated to frailty analysis, and is called ActFreeLi (detailed in section 2.4.2). Here, older adults wore a device during their daily routine in real world situations. Hence, the corresponding data, acquired in free-living conditions, were cut into 24-hour files. These data are analyzed to extract activity and health metrics in order to assess frailty conditions.

FallAllD for Activity Recognition

FallAllD, which stands for Fall in All Directions, is a dataset of human falls and ADLs, built by our team [START_REF] Saleh | Fallalld: an open dataset of human falls and activities of daily living for classical and deep learning applications[END_REF]. This large dataset consists of 26420 files, and thus is suitable for these high values, we can assess the effect of the sampling frequency on the performance of the system. As for the final product, researchers can evaluate their approach on lower frequencies by downsampling the acquired signals. This will be the case in the next chapter of this thesis.

It is worth noting that, since magnetometers measure magnetic fields, their sampling frequency could be relatively low compared to the other two sensors which measure the acceleration and the angular velocity (translational and rotational movements). However, it is recommended to use the same sampling rate for the accelerometer and the gyroscope. Moreover, a barometer was added to each data-logger, namely MS5607-02BA03 with high resolution module (20 cm). This sensor was configured such that B F s = 10 Hz and an operating range of 10 to 1200 mbar. Dataloggers used the MSP430F5528, a micro-controller by Texas Instruments. Therefore, this dataset covers several positions, and provides four different types of acquired data (acceleration, angular velocity, magnetic field, pressure) with a very large sampling frequency, thus outperforms the aforementioned publicly available datasets.

Protocol

Fifteen participants wore the three data-loggers simultaneously and simulated a set of falls and ADLs. The simulated falls were characterized following four parameters:

• Initial posture: inactive (sitting, standing, lying) and moving (walking, jogging, aiming to sit/lie down)

• immediately, (g) beating a table with a hand.

For each activity (fall or activity), the corresponding signals were cut using 20-second windows.

These windows are centered on the transition moment for transient ADLs, and on the peak (shock) for falls. This configuration of large F s and window length L is of great importance, since the effect of these two parameters on the reliability of the recognition system can be studied (by down-sampling F s and reducing L). In fact, since the activity is represented over 20-second windows and last only few seconds (around 2 seconds for a postural transition like sitting down for example), we can opt for data augmentation to train our machine learning models. By using smaller sliding windows, of 6-second length for example, we can segment the 20-second file into several 6-second samples considering that the transitions and the steps in a cyclic activity do not exceed the chosen window length (6-second length in our case). For instance, if we have a transient activity like lying down, we may consider a 6-second window centered on the transition moment, and several other windows shifted by few ms. In this case, the training set gets bigger and we are able to train the developed model on different scenarios,

i.e. when the transition moment is exactly in the middle of the window, and when the transition is somewhere in the left/right half of the window. This notion is meaningful, seeing that the sliding window is not controlled in real world situations (and this will be our case in the next chapter). For more details about data distribution, the reader may refer to Appendix D.

ActFreeLi for Frailty Analysis

ActFreeLi, which stands for Activities in Free Living Conditions, is a dataset of human movements, and it was also built by our team. It is a large dataset consisting of older adults' physical activity in free-living conditions during their daily routine. ActFreeLi is used to extract activity and health metrics in order to assess the physical condition of elderly and further the frailty status.

Devices and Characteristics

To collect data in free-living conditions, our partner RF-Track developed a second wearable device consisting of an accelerometer and a barometer. Unlike the previous dataset (FallAllD), the gyroscope and the magnetometer were excluded to reduce the power consumption. Seeing that the device will be used in real world conditions for long periods, our goal was to ensure a long autonomy so that the elderly will not have to recharge the device on a regular basis. In this case, we hope that the loss of data will be limited and that the elderly will end up accepting the device and wearing it as much as possible. which can be worn around the neck or on the waist (body trunk). Raw data of both sensors are preprocessed by the ultra-low-power micro-controller STM32L431 from STMicroelectronics (with FPU).

Protocol

In a previous project called Silver@Home (2017-2020), fall detection was tackled. The goal was to develop an automatic fall detector, dedicated to frail elderly who are likely to fall. To evaluate the performance of the developed solution, data of frail elderly over 80 years old, residing in different French long-term care facilities, were collected. Each participant was monitored for 3 months, and was visited thrice during this period. He/she was asked a set of questions to assess his/her psycho-cognitive health and his/her physical condition. These experiments lasted from May 2019 until March 2020.

In the ACCORDS project (2018-2022), another cohort is targeted, particularly healthier community-dwelling elderly over 80 years old. The idea is to monitor 30 recruited participants for 2 years (24 months M 1,...,24 ), in order to define and follow the frailty trajectory (the transition towards frailty). Data collection was supposed to start in March 2020, but was postponed for 6 months (September 2020) due to the pandemic of covid-19. The target was to launch the experiments with 80% of the recruited population being robust and the remaining 20% being pre-frail. On the day of inclusion M 0 , I visit the subject as a research scientist, accompanied by a specialist in psychology and a geriatrician, in order to introduce the material, to explain the experimental protocol, and to answer his/her questions. The participants are then visited thrice during those 2 years (at M 1 , M 12 , and M 24 ) by the specialist in psychology to assess their psycho-cognitive health as well as their sentimental state and the acceptability of the monitoring system. Additionally, they are visited every 3 months by a geriatrician, whose task is to assess their health conditions. Specifically, FrP, SPPB, and PSQI are considered to assess the frailty status, physical condition, and the quality of sleep respectively. Here, when a subject is characterized as being frail (based on the score of FrP), he is excluded from the study. Finally, I have to visit the subject once between two consecutive visits made by the geriatrician, in order to collect data, upload them to the secured server of LTSI called Ascent, and format the memory cards. It is worth mentioning that some data were lost due to several lockdowns, since the authorized team was not able to intervene and extract data. Hence, µSD cards were full and the corresponding wearable devices were not able to save new acquired data. Moreover, several subjects forgot to recharge their devices, which also led to data loss. Nonetheless, the dataset is large enough to conduct our study. Now, in both projects, the participants wore the previously described device (whose PCB is illustrated in Figure 2.6) during their daily routine without any specific instruction. Acquired data, which are saved on a µSD card, are cut and stored as 24-hour files. Therefore, each recording file represents a typical day of the device wearer in free-living conditions. Note that the use of frail people data was approved by the Ethics Committee of the University Hospital of Rennes,

France while the use of data collected under the ANR project, was approved by the Ouest VI Institutional Review Board of Morvan University Hospital of Brest, France. Consequently, data coming from both projects are combined to constitue ActFreeLi.

In conclusion, for monitoring and recognition systems, different combinations (thus inertial systems) can be used when it comes to the sensing unit: (1) accelerometer, (2) IMU {accelerometer + gyroscope}, (3) MARG {accelerometer + gyroscope + magnetometer}. Additionally, a barometer can be added to one of those three combinations to track the altitude of the wearable device. In this chapter, we have seen that MEMS accelerometers are preferred to PEC ones, since they measure the static acceleration (1 g) linked to the Earth gravity. Moreover, an AHRS can be formed based on an IMU or a MARG sensor, which is able to estimate the orientation of the device relative to Earth frame, using an orientation filter. Although such technique provides valuable contextual information, the power consumption is a major drawback due to the large current consumed by the gyroscope, as well as the reliability of magnetometers in indoor environments. Furthermore, the sensor placement can affect the acceptability as well as the accuracy of a recognition system. The body trunk has been chosen as the best position for a reliable recognition process, based on several experimental and scientific justifications. Now, it is worth mentioning that the software implementation (such as preprocessing and feature extraction)

and the choice of machine learning classifiers affect the computational complexity (in flops) of HAR algorithms, thus their embeddability in wearable sensors, their behavior in real-time, and the power consumption of the device. These operations are delicate, and the trade-off between complexity and accuracy should be taken into consideration. Finally, since representative data are needed for reliable solutions, two datasets were created to serve both modules, i.e. HAR and frailty analysis. The first one is called FallAllD, and it constitutes the basis of our developed HAR solutions (in terms of training, performance evaluation, and the effect of hardware configuration on the accuracy). The second one is called ActFreeLi, and it is used to associate activity metrics with frailty conditions and to evaluate the ability of our techniques to detect physical worsening via wearable sensors. In the next chapter, we explore the technical part of the HAR techniques. Once acquired and preprocessed, data will be subject to a recognition process in order to predict the performed activity over a sliding window. Different approaches are proposed, based on both deep learning and shallow learning techniques. The next chapter highlights these solutions, displays the experimental results and the performance evaluation, and discusses the developed prototype for each technique. Finally, it describes how the output of this HAR module is provided to feed the next module, which analyzes the localized ADLs to detect physical worsening and assess the frailty conditions of a subject. and applying machine learning models such as Random Forest (RF), Gradient Boosting Machine (GBM), Naive Bayes (NB), Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) to name a few. A prototype is then developed for each of these two techniques in order to highlight their behaviors in real world conditions.

The Targeted ADLs

Since the target is elderly care and surveillance of old people, the monitoring system should aim at analyzing (i) the postural transitions, (ii) cyclic/recurrent movements, and (iii) inactivity periods. Hence, the considered activities are basic ADLs which are encountered during daily routine of elderly, namely staying still (inactive), sitting down, standing up, lying down, rising up (transient ADLs), walking, jogging, and using the stairs (cyclic ADLs). Now, for cyclic ADLs, it is obvious that walking and using the stairs are close to each other from an acceleration point of view. When it comes to jogging, the acceleration patterns are quite different. Figure 3.2 illustrates the acceleration magnitude ||a|| resulting from jogging and walking respectively. It is worth mentioning that while a person is jogging or running, the range of ||a|| is significantly higher than while she is walking or climbing/descending the stairs. This observation is clearly pictured in this figure. Thus, the variability of the first type of cyclic activity is bigger than the two latter ADLs. Furthermore, the human body leaves the floor for a short time while jogging, contrarily to the other three activities (Z. [START_REF] He | Weightlessness feature -a novel feature for single tri-axial accelerometer based activity recognition[END_REF].

Weightlessness is a condition met when the effect of gravity is canceled by inertial force, like in free-fall. Hence, when the human body quits the ground for a short time, and on its way back, the value of acceleration magnitude ||a|| is close to 0 g. For example, we have 5 weightlessness intervals in the yellow window when the subject is jogging, two of them being spotted by red 0.78 g 3.22 g Jogging Walking walking, going upstairs or downstairs (C-3) and also from jogging (C-4). To ensure a practical solution, the swimming activity has been neglected since it is not considered as a regular activity for older adults.

Peak Detection

In order to choose the acceleration component over which the analysis should be done, the range R λ (∀λ ∈ {X, Y, Z}) of each component a X , a Y and a Z , i.e. R X , R Y , and R Z , is calculated using 3-second windows. Three scenarios may occur in this case:

• If all ranges are below 0.3 g (i.e. R λ < 0.3 g ∀λ ∈ {X, Y, Z}), the subject is supposed to be inactive in the 3-second interval under test, thus the window is labeled as 'inactive'. • If not, the only selected component is the one with the biggest range R λ , indicating that the performed activity has occurred over it. This choice makes the algorithm rotation-invariant, meaning that the performance is not affected if the device rotates around the wrist or if it is worn on any hand. The picked 3-second windowed acceleration signal is denoted as a λ , and is decomposed into eleven half-second (500 ms) segments s k (k = 1, ..., 11) with 50% • If none of the two previous situations occurs, we may be concerned by a cyclic activity.

Signal

Cyclic

Then we proceed to the peak detection.

Afterwards, a novel low-cost peak detection technique is applied, that preserves the shape of the signal a λ . For the remainder of this section, a λ (j) denotes the j th point of a λ which contains 3×F s points (since 3-second windows are used for prediction). Hence, considering 2

≤ j ≤ (3 × F s ) -1,
the method begins by recognizing the following points a λ (j):

a λ (j) > a λ (j -1) & a λ (j) > a λ (j + 1) (3.1)
as maxima in the signal. These points are then stored in an array P. Afterwards, the selected points should be scanned in order to retain the ones that actually represent the targeted peaks in the signal. We consider a segment τ of length l = 2L, centered on a λ (j). If no point in τ exceeds the value of a λ (j), the latter is declared as a peak. If not, it is removed from the array P since it is an outlier. The remaining points in this array are the actual peaks. To calculate the value of L, the following function is applied:

L =    2Fs 5 if R λ ≤ 1.25 g Fs 2R λ if R λ > 1.25 g (3.2)
with R λ being the range of a λ (the component with the highest range).

This criterion means that if the range R λ of the signal is less than 1.25 g, we should check 800 ms around each a λ (j) in P. When this range increases, the length of the segment decreases. This dynamic length is important in this context, because for activities showing high ranges (the case of Jogging and Clapping in Figure 2.3 for example), two or more peaks might occur over 800 ms, and consequently we should apply the scan on a smaller length. However, that is not the case for Walking, where the range is much smaller (≈ 0.67 g < 1.25 g). Note that when a λ (j) is close to the left end of the signal, the length of τ is less than 2L and it is no more centered on a λ (j) (the length of such segment in this case is l = L + j -1 < 2L). This remark holds for a λ (j) whose abscissa is close to the right end of the signal. Figure 3.4 illustrates a signal, with the points satisfying Eq. (3.1) (red crosses) and the remaining points after the scan, that are the actual peaks in the signal (black circles). In this example, the sampling frequency is 48 Hz. The range R λ of the signal is equal to 2.15 g. Hence, L = 12 (equivalent to 250 ms) which means that the segment τ is of length 500 ms. When τ is centered around the third actual peak (whose abscissa is approximately 1.5 s), the remaining peaks which fall between 1.25 s and 1.75 s are excluded. Now, if one or zero peak is detected in a λ , the window is also labeled as 'Transient'.

If not, we proceed to feature extraction to classify this cyclic activity.

Feature Extraction

Four handcrafted features are extracted after the previous operations, in order to characterize the peaks and the corresponding valleys (space between two peaks) and classify the activity.

Prominence:

The prominence is defined by the intrinsic height of a peak and its location relatively to other peaks. Suppose t is the location of a peak pk. Two intervals from both sides of pk should be defined: Ī1 = [t l , t] and Ī2 = [t, t r ]. t l is the location of the closest higher peak on the left side of pk (or the left end of the signal if no higher peak is found). t r is the location of the closest higher peak on the right side of pk (or the right end of the signal if no higher peak is found). The reference level (RLv) (see Figure 3.5.a) is the higher of these two intervals minima.

The prominence feature is the height of pk above this level.

Width: To measure the width of the peak, the half prominence (HPr) (Figure 3.5.a) is used as reference. This second feature, i.e. the width of the peak, is the difference between the abscissa of the first point at the right side of the peak, having this reference as an ordinate, and the one of the first point at the left side of it. These abscissas are estimated by interpolation.

Variability: this low-cost feature estimates the variability between two peaks for a given signal. Suppose that Dx is the array containing the differences between two consecutive points (see consecutive values in Dx have different signs. The variability feature is defined by the ratio M N . Entropy: The unpredictability or the randomness of an acceleration signal is a key to discriminate between two behaviors. For example, for activities requiring hand-waving, the movement of the wrist is regular. This is no more the case when the subject is walking, since the wrist moves arbitrarily. In the literature, the multiscale entropy is considered as a measurement to analyze complex physiological time series [START_REF] Costa | Multiscale entropy analysis of complex physiologic time series[END_REF]. Here, we calculate the distribution entropy of the selected acceleration component, which represents the fourth feature. with some interferences between some pairs of clusters. For example, Walking is defined by its small prominence, while Clapping is defined by its high prominence and small width and so on. DT is adequate to classify these four behaviors, as it compares one of the features with a threshold, at a certain node, to make a decision until we reach a leaf. However, it may cause confusion in the different interference regions. This 2D space can be divided into 5 different clusters as shown on this figure. Two out of five clusters represent a Zone Of Interference (ZOI), where data points of activities belonging to two different classes fall in. ZOI (I) contains data points of classes (C-2) and (C-3), while ZOI (II) is a mix of both classes (C-1) and (C-4).

Classification Process

Thus, further investigation is needed to discriminate between the two classes in each of these two ZOIs. Regarding ZOI (I), the unpredictability of the acceleration signal is estimated, thus a third dimension is added. This feature is important to discriminate between (C-2), showing regular acceleration signals (Waving in Figure 2.3), and (C-3), showing irregular or complex acceleration signals (Walking in Figure 2.3). Figure 3.6.b illustrates the 3D space by adding the entropy as a third dimension with a 3D linear SVM hyperplane separating these two classes (upper graph), and its intersection with the 2D plane determined by the Entropy and the Width (lower graph). Regarding ZOI (II), and since the differences between two consecutive points is smaller for activities belonging to class (C-1) compared to the ones belonging to class (C-4) (Figure 3.5.c), the variability is computed in this case, and added as a third dimension. Figure 3.6.c illustrates the distribution in this 3D space with a quadratic SVM hyperplane separating these two classes. Taking these remarks into account, we propose a novel machine learning design acting as follows (see Figure 3.7): the mean values of the prominence and width are calculated and introduced to a trained DT. This tree takes the decision and classifies the activity accordingly.

If it leads to ZOI (I), the entropy of the acceleration signal is computed, and this feature vector of length 3 (Width, Prominence and Entropy) is introduced to a trained linear SVM (SVM L ) that classifies the corresponding activity. If it leads to ZOI (II), the variability is calculated, and the feature vector of length 3 (Width, Prominence and Variability) is introduced to a trained quadratic SVM (SVM Q ). Otherwise, the activity is labeled according to the prediction done by the DT. This architecture decreases the complexity since the third feature is extracted and the SVM is applied only if needed.

Experimental Results

FallAllD was used to validate the proposed method. Acceleration data representing the four classes were selected then segmented using 3-second windows with 83%-overlapping (2.5 s). These signals were downsampled by a factor of 4, leading to F s equal to 60 Hz. The proposed peak detection technique was applied then feature extraction was done, before testing the classification architecture represented in Figure 3.7. A 10-fold cross validation was adopted to evaluate the performance of the proposed approach. The model achieved an accuracy of 97.08% using the aforementioned configuration. Figure 3.8 illustrates the resultant confusion matrix, where the columns represent the actual classes, and the rows represent the output of the algorithm (i.e.

the predicted classes). For instance, 2% of clapping hands (C-1) were classified as walking (C-3).

The two highest confusions occur between (i) clapping (C-1) and waving hand (C-2) (equal to 5.9%) and (ii) waving hand (C-2) and walking (C-3) (equal to 9%). It is worth mentioning that, on average, the SVM was called 41.87% while classifying windowed acceleration data. In other words, around 60% of data in the test sets do not fall in ZOI, and thus the prediction is made by the DT model (using only two features).

To extend the experiments, I wore a wrist-worn device produced by RF-Track and simulated some activities which might occur during daily routines of elderly. A wide range of ADLs was covered, belonging to each of the four defined classes. windows with a squeegee, cleaning tables with a towel, and waving goodbye are represented by some hand-waving (C-2). In addition to those activities, walking, going upstairs and downstairs (C-3) and jogging (C-4) were also simulated. Inactivity was also tested by performing activities requiring small movements like typing on a keyboard, chatting on a smartphone and sleeping. I wrote down the cyclic activities performed with the corresponding date and time, and acquired signals were annotated manually. The algorithm has the ability to detect inactivity periods correctly and to discriminate them from transient activities. For example, when I was sleeping, windows containing transient behaviors like turning while lying or changing position are not confused with windows where I was not moving at all. As for cyclic activities, 5913 decisions were made. The second stage of the algorithm (extracting one of the variability/entropy features and applying the SVM) occurred 1742 times (29.5%): 1363 for entropy then SVM L and 379 for variability then SVM Q . This shows the effectiveness of the proposed architecture in terms of complexity. The algorithm succeeded with an accuracy of 93.74% with cyclic activities.

The experimental results show the effectiveness of the proposed approach under supervised conditions. Nevertheless, several limitations and drawbacks are noted. The four classes were simulated following a predefined experimental protocol. Hence, the achieved accuracy might not necessarily reflect the performance of the system in real world situations. As discussed earlier, the arm can move randomly when performing an activity like walking for example, which may affect the pattern of the signal and thus lead to a misclassification by the proposed algorithm.

Moreover, postural transitions are not captured from this location. The body posture, which can be a sensitive point in our context, is not accurately estimated by this sensor. Besides, the successive movements of the trunk (for gait analysis and the estimation of activity rate for example) reflects the prevalence of frailty, unlike the movements of the arm/wrist. Therefore, this device is not really satisfying for frailty screening, and ADLs should not be analyzed from this position. Consequently, a deeper recognition process is discussed in the next sections, using a trunk-placed device.

Trunk-placed Tracker

Attitude-based Recognition Approach

One way to monitor the physical activity is to estimate the orientation of the wearable device.

Therefore, a step by step recognition method is proposed (Abbas et al., 2021), which (a) ensures a smooth visualization of the wearable device (sensing unit) in real-time and (b) makes a decision each second by predicting the performed activity over a sliding window. It is based on a 9-DoF inertial system, i.e. MARG sensor. Since data are acquired using different sources/sensors, two configurations (λ i ) can be considered, depending on the sampling frequency of the accelerometer A F s , the gyroscope G F s , and the magnetometer M F s :

   A F s = G F s = M F s (λ 1 ) A F s = G F s > M F s (λ 2 )
Generally, researchers opt for the same sampling frequency for all modalities (configuration λ 1 ).

Nevertheless, the sampling frequency of the magnetometer could be lower as seen in the previous chapter. This is the case for FallAllD, which was constructed using configuration λ 2 . Therefore, we make sure that our method operates for both configurations. Figure 3.9 illustrates the order of data-points acquisition (acquisition cycle) following both configurations.

Orientation Estimation and 3D Visualization

To display the wearable device in real-time, a platform was developed. (x, z) is the plane of the screen, and y is the axis perpendicular to the aforementioned plane. The enclosure is symbolized by a parallelepiped centered at the origin, by defining the coordinates of 8 vertices V i (x i ; y i ; z i ) (i = 1, ..., 8), and connecting them using the map M (as indicated in Figure 3.10):

V i =                                            V 1 (-1; -0.25; -0.
M =                              V 1 → V 2 → V 6 → V 5 V 2 → V 3 → V 7 → V 6 V 3 → V 4 → V 8 → V 7 V 4 → V 1 → V 5 → V 8 V 1 → V 2 → V 3 → V 4 V 5 → V 6 → V 7 → V 8
Moreover, the faces of the created body are indicated using the following labels (letters) in red

A G M A G M A G A G M Acquisition Cycle (𝜆 1 ) Acquisition Cycle (𝜆 2 ) A G A G M A G M A G M
Acquisition Cycle

A x = p x × C A ; A y = p y × C A ; A z = p z × C A 7: Q ← Madgwick filter; Q ← conjugate(Q) 8:
Estimate ψ, θ, φ from Q using ( 2) represents the orientation of the device while the subject was walking, whereas the second one (right graph) corresponds to the hit on the floor.

9: if type = 'G' then 10: G x = p x × C G ; G y = p y × C G ; G z = p z × C G 11: if type = 'M' then 12: M x = p x × C M ; M y = p y × C M ; M z = p z × C M 13: counter ← counter + 1 14: if counter = ξ then 15: B = patch(V i , M ); Assign labels η 16: d 1 = V 2 +V 7 2 ; d 2 = V 4 +V 7 2 ; d 3 = V 6 +V 8

Activity Identification

The attitude of the device (estimated Euler angles) over a period of time provides important clues in recognizing physical activities. The successive movements of the trunk should now be exploited to address the problem of HAR. The output of an HAR module depends on the application.

Since the target is elderly care and surveillance of old people, the monitoring system should aim at analyzing (i) the postural transitions, (ii) the cyclic/recurrent movements, and (iii) the inactivity periods as indicated in section 3.1. Explicitly, the considered classes are (C 1 ) sitting down (walk-to-sit and stand-to-sit), (C 2 ) standing up (sit-to-stand and sit-to-walk), (C 3 ) lying down (sit-to-lie and stand-to-lie), (C 4 ) rising up (lie-to-sit and lie-to-stand), (C 5 ) walking, (C 6 ) using the stairs (upstairs and downstairs), (C 7 ) jogging, and (C 8 ) inactive (standing, sitting, lying). Now, human beings might perform a wide range of activities or movements in their daily z-axis z-axis fall. These activities may induce some confusion with some of the output classes. Therefore, the developed solution must filter out these movements which are not concerned by our application.

As a matter of fact, jumping is an unusual activity for older adults, while fall detection does not bring an added-value in the context of frailty analysis (as explained in Chapter 1). Consequently, a ninth class (C 9 ), named others, is added to filter out the remaining activities, alongside other random movements like the beginning/end of a cyclic activity (i.e. walk-to-stand, stand-to-walk, start/stop jogging), which result from the overlap of the sliding window.

A 6-second window is chosen for the remainder of this section, i.e. a prediction is done after processing the movements over 6 s. This length is adequate since smaller windows may exclude informative parts for the recognition, while larger ones may contain a number of movements from different activities. On the one hand, the recognition could be done by extracting handcrafted time-domain and frequency-domain features from raw signals, to feed classifiers like RF, KNN, and DNN [START_REF] Mishra | Human activity recognition using deep neural network[END_REF][START_REF] Shoaib | Complex human activity recognition using smartphone and wrist-worn motion sensors[END_REF][START_REF] Zhou | Accurate recognition of lower limb ambulation mode based on surface electromyography and motion data using machine learning[END_REF]. Moreover, Random Subspace (RS) technique has been also proposed to process Quaternions and Euler angles [START_REF] Zmitri | Human activities and postures recognition: from inertial measurements to quaternion-based approaches[END_REF]. On the other hand, deep learning techniques like CNN [START_REF] Ha | Convolutional neural networks for human activity recognition using multiple accelerometer and gyroscope sensors[END_REF][START_REF] Jiang | Human activity recognition using wearable sensors by deep convolutional neural networks[END_REF], and recurrent networks like LSTM [START_REF] Mekruksavanich | Lstm networks using smartphone data for sensor-based human activity recognition in smart homes[END_REF][START_REF] Murad | Deep recurrent neural networks for human activity recognition[END_REF] have been also proposed. In this case, the feature extraction is done automatically. Here, we propose a novel recognition process, which is based on feature fusion (both handcrafted and automatically learned features) and a combination of several classification processes. The patterns of Euler angles, resulting from the sensor fusion technique (previous subsection), feed a recurrent network that is LSTM in our case. This network is able to learn and remember over long sequences. It supports three parallel time-series of input data, i.e. ψ, θ, and φ. This model learns an internal representation of the aforementioned sequences by extracting features automatically and mapping them to the nine activity classes. It is defined by a single layer of 100 units. Now, the orientation of the trunk may not be sufficient for an accurate identification. For example, the orientation of the human body while falling can be similar to the orientation while lying down in some situations. The speed of the movement and the shock resulting from the activity are an added value to increase the reliability of the recognition process. Such parameters are derived from the acceleration of the trunk. The filter size of the first layer is 9 × 3, while the filter size of the remaining layers is 9 × 1. Those layers are followed by Max Pooling layer, to reduce overfitting to the training data.

The benefit of deep learning techniques is their ability to learn automatically from raw data as mentioned before. They do not require strong expertise in feature engineering. Nonetheless, the handcrafted features resulting from feature engineering complement the learned features to add more knowledge for the classifier. Now, these handcrafted features are extracted from both data, i.e. Euler angles and acceleration. Accordingly, the acceleration magnitude ||a|| is first computed as a 2

x + a 2 y + a 2 z . Euler angles and ||a|| are split into three equal segments k of 2 s (k = 1, ..., 3) without overlapping:

(k) ψ, (k) θ, (k) φ, (k) ||a||, for k = 1, ..., 3

The mean values of { (k) ψ, (k) θ, (k) φ} and the standard deviations of (k) ||a|| are computed, resulting in 12 features. Additionally, the correlation between each pair of Euler angles {ψ, θ, φ} is computed. The same goes for each pair of {a x , a y , a z }. The last two operations result in 6 features. Finally, those 18 features are scaled using the following sigmoid function:

S(x) = 1 1 + exp(-x) (3.
3)

The scaled feature vector feeds a third unit consisting of three fully connected layers (Dense).

The numbers of neurons are 40, 20, and 10 respectively. The activation function of these layers is 'ReLu'. The outputs of these three networks are concatenated, in order to feed the output layer including a softmax function which generates a probability distribution over 9 classes to predict the output of the performed activity. Figure 3.12 illustrates the diagram of this identification technique, which is based on feature fusion (automatically learned features + handcrafted features). This method will be denoted as CDL (for CNN, Dense, LSTM) in the remainder of this thesis.

Performance Evaluation

FallAllD dataset was used in this experiment, taking both the necklace and waist-worn devices into account (body trunk). Hence, configuration λ 2 was used during these experiments, partic- fall while walking (standing), (ii) fall while sitting, and (iii) fall from bed (lying). This random shifting is important to train the model using different positions, seeing that a sliding window is used in real world conditions, and thus we cannot control the segmentation in real-time. As for cyclic ADLs (C 5 , C 6 and C 7 ), five random 6-second windows were considered, since the movements were recurrent (repetitive). These operations resulted in 9100 samples, which is sufficient in principle to train the model: 1150 as "sitting down", 1150 as "standing up", 770 as "lying down", 770 as "rising up", 1000 as "walking", 550 as "using the stairs ", 520 as "jogging", 1100

ularly A F s = G F s =
as "inactive", and 2090 non-targeted activities (others). A 10-fold cross validation was applied to evaluate the performance of our system. The networks were first trained on 90% of data (randomly chosen), using the RMSprop optimizer and the categorical cross-entropy as a loss function. The batch size was equal to 64. The trained networks were then tested on the remaining 10% of data (unseen data) and the accuracy was saved. This process was repeated 10 times, and the final achieved accuracy was denoted as the mean of the aforementioned accuracy values. Moreover, to demonstrate its efficacy, we compared our method with traditional techniques which were proposed in the literature. Specifically, we first tested deep learning techniques individually, particularly CNN and LSTM, which were fed by Euler angles and acceleration signals. Furthermore, shallow learning was also considered.

Expressly, the handcrafted features fed a DNN (Dense layers), using the architecture of [START_REF] Mishra | Human activity recognition using deep neural network[END_REF], and the widely-used KNN (k = 5) and RF (25 estimators). Finally, the RS technique was also tested, using 14 features, namely the values of quaternions and Euler angles (7 components) over half windows (7×2). All the aforementioned methods were implemented using tensorflow library on Python 3.6. Table 3.1 illustrates the corresponding accuracy (of this 9-class model) for each method, showing the superiority of the CDL fusion technique reaching 97.7% accuracy. As expected, the fusion between different types of features increases the discrimination power of the classification process. Additionally, analyzing the patterns of each type of input data by one specific network (a convolutional network for acceleration and a recurrent network for Euler angles) is adequate for HAR and leads to better performance. Now, Figure 3.13.a illustrates the confusion matrix of CDL. The columns represent the actual classes and the rows represent the predictions (the output of CDL). The main confusion (5.79%) occurs between walking and climbing/descending stairs. This was expected since both classes are quite similar in terms of acceleration and trunk orientation. Moreover, when the subject is using the stairs, the intensity of the movements significantly decreases when he reaches the staircase landings. This pattern resembles that of C 1 and C 2 to some extent, which explains the slight misclassification rate with these classes (0.76% -0.96%). To solve this issue, the number of DoFs should be increased, following two ways: either (a) by using another device located on the thigh or the ankle for example, since the movement of the leg while using the stairs differs from walking and/or sitting/standing, or (b) by mixing C 5 and C 6 into one class while adding another sensor, namely a barometer, which can measure the difference in altitude in a post-processing module. Figure 3.13.b illustrates the confusion matrix after mixing C 5 and C 6 . In this case, 3.1). Particularly, CDL remains the top performer with an accuracy of 98.68%. Hence, in the case of the 8-class model, barometric data are checked when the output is C 5 , in order to see whether the altitude is increasing/decreasing in the sliding window (i.e. using the stairs) or not (i.e. walking). Note that this 8-class model could be sufficient for a wide-range of medical applications. It is worth mentioning that another noticeable confusion is the one between sitting down and standing up (1.16% -1.36%), particularly standto-sit and sit-to-stand. This problem is also resolved by adding a barometer, since the altitude decreases/increases when the subject sits/stands.

Acceleration-based Recognition Approach

It is clear that the computational load of the previous method is heavy. It needs to be executed on a remote server with high power resources in order to operate in real-time. Hence, a new practical and low-cost solution is proposed in this section (Abbas and Le Bouquin Jeannès, 2021) to meet industrial constraints and to be embedded in the device. Seeing that (1) our partner RF-Track is specialized in the design and manufacturing of ultra low power smart connected sensors and ( 2) the experimental setup of ACCORDS project (continuous monitoring over 2 years) requires a device with a long autonomy, this approach is based solely on acceleration signals (low power consumption) with a low computational load. It serves the same purpose as the previous one, i.e. a step by step recognition in unsupervised conditions.

Problem Formulation

We follow the same logic in this approach, i.e. detecting inactivity periods, as well as cyclic and transient ADLs. Nonetheless, seeing that the input has changed (from 9-DoF to 3-DoF inertial system), some changes are made to the classification process. The targeted ADLs are the same, expressly (C 1 ) sitting down, (C 2 ) standing up, (C 3 ) lying down, (C 4 ) rising up, (C 5 ) walking (same level, climbing up, climbing down), (C 6 ) jogging, (C 7 ) inactive (standing, sitting, lying) and (C 8 ) others. Although the number of DoFs is reduced after excluding the gyroscope and the magnetometer from the acquisition unit, the acceleration signals can be adequately exploited to classify the different activity patterns accurately, using machine learning techniques (Abbas et al., 2020).

The goal behind the proposed model is to regroup the targeted activities into different clusters at each level, creating a tree structure classification process. This strategy aims at increasing the discrimination power of the system. Figure 3.14 displays an organizational chart that shows the possible movements of an elderly captured from a trunk-placed accelerometer. E). Moreover, the acceleration component directed towards the human trunk fluctuates when the subject sits/stands. This is not the case for other similar non-postural transitions. Figure 3.15 illustrates the acceleration patterns of sitting down and standing up. In the next subsections, we detail the features to be extracted from the acceleration signals in order to discriminate between the different output classes and we present the proposed algorithm which transposes the organizational chart of Figure 3.14 into a novel and optimized classification process.

Local Temporal Characteristics

To employ the temporal characteristics of an activity, the first and second order moments of its corresponding time-series are considered, namely the mean value µ and the SD value σ:

µ = 1 n n i=1 V i (3.4)
contains faster transitions, as shown in Figure 3.15 (fast sine wave transition in ||a|| vs slower deviation in a Z ). As for the intensity of movements, local SD values are calculated over 1-second segments of ||a||, seeing that σ is sensitive to random fluctuations over very small sub-segments (like 500 ms), which might raise the confusion between the output classes.

Consequently, the succession of these mean values reveals the trunk orientation, the up-down movements, and locates the weightlessness states and the deviation in a signal. Furthermore, the succession of SD values detects the sudden change in movements intensity and estimates the variability of time-series. As discussed in the previous subsection, these parameters are important to increase the discrimination power of the system. The ambiguity between different activity classes is expected to decrease considerably using the proposed local feature extraction.

Online Feature Computation

The goal of this subsection is to describe the online feature extraction technique, i.e. the calculation of local mean and SD values in parallel with data acquisition. Figure 3.16 illustrates the process of online feature computation for a given acceleration component. The idea is to store data in m buffers ζ [i] of length n, which represent the local segments over which the features are calculated, and to update the elements of a vector χ, which will be used to create the feature vectors when making a decision. With each new acquisition, i.e. when the accelerometer provides a new data-point, a new value ν is introduced by shifting ζ

[i] j as indicated in Figure 3.16, and the values χ i are updated:

χ i ← χ i -ζ [i] 1 + ζ [i]
n . Algorithm 3 shows the pseudo-code of this process.

Algorithm 3 Online Feature Computation

1: Define: L, F s , counter = 0 2: Initialize: Λ [i] , Υ [i] , λ, ρ are set to 0 3: while true do 4:

Read acquired acceleration value

V i 5: ν ← V i 6: Shift values Λ [i] j ; Λ [m] n ← ν 7: λ i ← λ i -Λ [i] 1 + Λ [i] n 8: ν ← V 2 i 9: Shift values Υ [i] j ; Υ [m] n ← ν 10: ρ i ← ρ i -Υ [i] 1 + Υ [i] n 11: counter ← counter + 1 12: if counter = F s then 13:
Calculate µ i and σ i according to Eqs. 3.6 and 3.7

Moreover, buffers Λ

[i] j are considered to store acquired acceleration data-points V i . λ i = n j=1 Λ

[i] j is updated with each new acquisition. In this case, we get:

ν ↔ V i ; ζ [i] j ↔ Λ [i] j ; χ i ↔ λ i
µ i = c × λ i (3.6)
SD values: in addition to Λ

[i] j , new buffers Υ

[i] j are considered to store V 2 i values. Therefore,

ρ i = n j=1 Υ [i]
j is updated with each new acquisition. Hence, we get:

ν ↔ V 2 i ; ζ [i] j ↔ Υ [i] j ; χ i ↔ ρ i

Propagation \zeta and \chi

Buffers 

[𝑖]

 1 [1]  2 [1]  𝑛-1 [1]  𝑛 [1]  1 [𝑚]  2 [𝑚]  𝑛-1 [𝑚]  𝑛 [𝑚]  1  𝑚  𝑖 ←  𝑖 - 1 [𝑖] +  𝑛 [𝑖]
Vector    𝑗 [𝑖] \ 𝑖, 𝑗 = 1 → 𝑚, 𝑛 1 is excluded, and the elements χ i are updated as indicated in the figure .  Here, ||a|| is involved, with m = L and n = F s . Consequently, at each decision, the SD of the i-th segment (i-th second) is calculated based on ρ i , λ i , and c (Eq. (3.7)):

σ i = c(ρ i -cλ 2 i ) (3.7)

Multinomial Decomposition Algorithm

With online extraction, 5L local features are calculated automatically in parallel with data acquisition. For instance, with a 5-second window (L = 5), 25 features are computed and stored in an array F (see Figure 3.17). Suppose that F i is the i th element of F , the extracted features are as follows:

• µ values of a X over each second in the L-second sliding window (denoted by F 1,...,L , i.e.

first L elements of F )

• σ values of ||a|| over each second in the L-second sliding window (denoted by F L+1,...,2L )

• µ values of ||a|| over each 500 ms in the L-second sliding window (denoted by F 2L+1,...,4L )

• µ values of a Z over each second in the L-second sliding window (denoted by F 4L+1,...,5L )

The proposed Multinomial Decomposition Algorithm (MDA), which exploits the aforementioned features to predict ADLs, is now introduced. This low-cost algorithm divides the multinomial classification into different stages, where the encoded patterns feed a Neural Network (NN) at each stage to classify the corresponding segment.

Classifier: an artificial NN is called at each level of the tree-structure classification process to make a prediction, until it reaches a leaf. This NN consists of one hidden layer of 10 neurons, with a customized transfer function h (x) detailed in Appendix F. It is derived from the hyperbolic tangent sigmoid, after introducing an expansion of exponential to reduce its computational

𝐹 1 … 𝐹 𝐿 𝐹 𝐿+1 … 𝐹 2𝐿 𝐹 2𝐿+1 … 𝐹 4𝐿 𝐹 4𝐿+1 … 𝐹 5𝐿 𝜇 of 𝑎 𝑋 𝜇 of ‖𝑎‖ 𝜇 of 𝑎 𝑍 𝜎 of ‖𝑎‖ Figure 3
.17 -The 5L extracted features using online computation.

(III) Transient. (I) is a leaf, and its corresponding output is "Inactive". Next, mean values of a X and SD values of ||a|| (F 1,...,2L ) feed the NN to assign a second-level label (S2), namely (a) Orientation, (b) Intensity, and (c) None. The activity reaching (a) is either "Lying down" or "Rising up", depending on the direction of the transition, whereas that reaching (b) is filtered out. Finally, the third-level stage (S3) depends on the previous attributes. For ADLs belonging to (II-c), a third NN, whose inputs are the mean and SD values of ||a|| (F L+1,...,4L ) is applied, to see whether the subject is "Walking" or "Jogging". As for (III-c), the inputs of the third NN are the mean values of ||a|| and the mean values of a Z (F 2L+1,...,5L ), to see whether the subject is "Sitting down" or "Standing up", or if the activity is to be excluded (non-postural transition).

Performance Evaluation

MDA was tested on FallAllD by applying a 10-fold cross validation, using the same segmentation for transient (centered on the transition moment + random shifting) and cyclic (random windows) ADLs as explained in section 3.3.1.3. The aforementioned operations resulted in 9100 samples: 1080 as "sitting down", 1080 as "standing up", 720 as "lying down", 720 as "rising up", 1130 as "walking", 520 as "jogging", 1095 as "inactive", and 2755 non-targeted activities (others). The achieved accuracy is reported as a heat map in Hz). MDA attains high accuracy (around 97-98%) which is quite satisfactory for frailty analysis, proving its efficiency in terms of reliability. To assess the influence of the output class on the performance of MDA, precision and recall were calculated as displayed in Figure 3.20. For each class (C i ), suppose that CP i is the number of correctly predicted samples (belonging to (C i )), AP i the total number of samples labeled as (C i ) by the algorithm, and AS i the actual samples belonging to (C i ), hence:

   precision(C i ) = CP i AP i recall(C i ) = CP i AS i (3.8)
These two metrics present the lowest values (between 0.94 and 0.96) when it comes to sitting down and standing up. Now, MDA is highly sensitive to inactivity periods (highest recall) and is highly precise when it comes to cyclic ADLs. Now, we compare MDA to a wide range of handcrafted features and state-of-the-art shallow learning and deep learning techniques to assess its efficiency. Particularly, we tested the following well-known handcrafted features from time and frequency domains, denoted as HFeats, which have been shown to be effective [START_REF] Banos | Design, implementation and validation of a novel open framework for agile development of mobile health applications[END_REF][START_REF] Bonomi | Detection of type, duration, and intensity of physical activity using an accelerometer[END_REF][START_REF] Xie | Human activity recognition method based on inertial sensor and barometer[END_REF]; J.-Y. Time-domain: mean, SD, median absolute deviation, maximum, minimum, energy, interquartile range, and entropy for each of the three components; the first four autoregressive coefficients of ||a||; correlation coefficients between each pair of two components; signal magnitude area.

Frequency-domain: largest frequency component, weighted average, skewness, kurtosis, and energy for each component; angle between the acceleration components taken two by two. This comparison helps proving the efficacy of local temporal characteristics in HAR. These large feature vectors are tested to see their effects on the performance. Moreover, we considered the following techniques:

• classical classification strategy (CCS) with one NN using the proposed feature vectors F 1,...,5L (section 3.3.2.4), i.e. one stage of 8-class classification instead of dividing the problem into subdivisions like MDA.

• 9 shallow learning classifiers, namely NN (1 layer of 10 neurons), SVM (polynomial order 3), KNN (k = 3), RF (20 estimators and maximum depth equal to 10), GBM (100 estimators and maximum depth equal to 5), DT, NB (Gaussian distribution), LDA, and QDA.

• CNN using raw acceleration components.

• simple RNN, LSTM, and GRU using raw data.

• Stacked AutoEncoder (SAE) of dense layers.

• feature fusion (FeFu) as in (Z. [START_REF] Chen | Smartphone sensor-based human activity recognition using feature fusion and maximum full a posteriori[END_REF]. Now, the performance of deep learning models, especially recurrent ones, depends on data size. Therefore, the considered models were trained and tested on the same 9100 samples, i.e. training and test sets (TrSet and TeSet) were the same. Table 3.2 illustrates the accuracy of each model. It is obvious that the accuracy of RNN is poor. The performance of LSTM is somewhat better, but still not satisfying. This was expected since simple RNN may suffer from vanishing/exploding gradient problem, while LSTM might need larger datasets (depending on the application and the type of acquired signals) to learn properly. However, GRU avoids both problems. CNN and SAE were also able to train, displaying quite high performance. Therefore, in a second step, only CNN, GRU and SAE were kept and a 10-fold cross validation was applied on FallAllD. In this step, the aforementioned nine shallow learning techniques were also tested for comparison, considering the 50 handcrafted features (HFeats) extracted from windowed data. The FeFu technique combined GRU with HFeats. All these classifiers were trained then tested using all (F s , L) pairs. Table 3.3 illustrates the highest accuracy achieved by each model, where the top 3 values are underlined. MDA is amongst the best performers, by providing competitive results.

SAE is the worst deep learning model in terms of performance. As expected, FeFu outperforms GRU since it adds another dimension to the recognition process (as explained when introducing CDL). KNN and GBM are the best performers with excellent accuracy when it comes to shallow learning models. Furthermore, for CCS, the proposed feature vectors, i.e. local mean and SD values, were concatenated to form one vector of length 5L, which constituted the input of a NN with one hidden layer of 10 neurons. This is the case of traditional machine learning methods,

where extracted features feed one single classifier. In this case, the accuracy drops from 98.03%

(MDA) to 95% (CCS). This proves the added-value of the proposed classification architecture.

Encoding the temporal characteristics is valuable, since the achieved accuracy of 95% is still relatively high, but the way of interpreting them plays a huge role in improving the performance.

On the other hand, Figure 3.21 illustrates the variation in accuracy while fixing F s and increasing L (left graph), and while fixing L and increasing F s (right graph) for MDA, deep learning models and the two best shallow learning performers (GBM and KNN). It is clear that very tight windows are not suitable for HAR. Now, for CNN, GBM, and KNN, larger windows increase the accuracy. However, for recurrent networks (GRU) and SAE, the ideal L is somewhere in the middle, since relatively larger windows make the accuracy decrease.

Furthermore, in general, the accuracy increases while increasing F s , except for SAE, since its accuracy is saturated around 89%. This is logical since higher F s provides more data-points in Figure 3.21 -The achieved accuracy (%) when (i) F s is fixed and L is variable (left graph) and (ii) L is fixed and F s is variable (right graph).

time-series. Hence, the pattern of signals delivers better knowledge to the machine. Note that, for shallow learning models, the accuracy is somewhat the same for F s ≥ 40 Hz. It is worth mentioning that a deeper CNN is required for higher sampling frequencies [START_REF] Saleh | Fallalld: an open dataset of human falls and activities of daily living for classical and deep learning applications[END_REF], since the features extracted by the first layer is more local and thus a deeper architecture is needed to abstract them. This examination is important to choose the best configuration for a HAR system.

Overfitting

The overfitting phenomenon occurs frequently in machine learning. If the learning corresponds too closely to a particular dataset, it may fail to fit additional data or predict future observations accurately. Thus, the choice of extracted features and the classifier is delicate. Since 10-fold cross validation may not reveal overfitting, seeing that training and testing are done on data from the same sensing unit, same subjects, and under the same conditions (same clinical trial), we suggest another experiment. The aforementioned models were trained on FallAllD, then tested on four different public datasets, namely Sisfall (Sucerquia et al., 2017), mHealth [START_REF] Banos | Mhealthdroid: a novel framework for agile development of mobile health applications[END_REF][START_REF] Banos | Design, implementation and validation of a novel open framework for agile development of mobile health applications[END_REF], HAPT (Anguita et al., 2013), and UMAFall [START_REF] Casilari | Umafall: a multisensor dataset for the research on automatic fall detection[END_REF]. Table Table 3 selected for each activity. For transient activities, the centers of the 3 selected windows were randomly set between the transition moment ±500 ms (to replicate the behavior of sliding windows in real world conditions). For cyclic activities, the windows were selected randomly over the period of these movements.

Table 3.5 illustrates the accuracy of deep learning models (CNN, SAE, and GRU), top two shallow learning performers (KNN and GBM), FeFu, and MDA on each dataset, where values exceeding 90% are in bold. On the one hand, shallow learning methods are generally exposed to overfitting when tested on completely unseen data. This is obvious since the features are extracted globally from windowed data. Hence, they reflect the statistical patterns of a signal without taking into consideration its temporal structure, which may lead to undesirable confusion between different classes. Moreover, large feature vectors may mislead the machine. On the other hand, the performance of deep learning models is considerably better. Particularly, recurrent networks are more robust since they learn and remember over time sequences, contrarily to CNN for example, which exploits the spatial correlation of data. Finally, MDA avoids overfitting since it encodes local temporal characteristics, and thus provides much better results than most of the other approaches. It is worth mentioning that results on mHealth show relatively higher performance. The detection of recurrent movements and inactivity periods is easier than that of transitions. In conclusion, high accuracies may not always reflect the behavior of the system in real world conditions. This experiment was important to show the importance of extracting local features from acquired signals (the case of both methods CDL and MDA) instead of feeding classifiers with large feature vectors that are computed globally from windows.

Table 3.5 -Accuracy when the methods are tested on FallAllD using a 10-fold cross validation (TeSet ← → 10-CV), and when the training is done on FallAllD and the testing on the remaining datasets (TeSet ← → {Sisfall, mHealth, HAPT, UMAFall})

Computational Cost

Ultimately, we measured the computational time of the aforementioned models.

Execution Time: We ran a Python 3.6 implementation of the algorithms on an Intel(R) Xeon(R) Gold 5118 2.3-GHz processor with 64 GB RAM. Table 3.6 illustrates the elapsed time during the training phase and feature extraction + prediction phase on 9100 samples. KNN is the fastest when it comes to training, since it only places the labeled vectors in some metric space. However, classifiers are trained offline. Hence, this phase is not related to the latency of the system. On the other hand, it is clear that MDA provides the fastest response when it comes to predicting the activity, and it is negligible compared to most of the other techniques.

With the efficient online computation technique and the tree-structure classification process, the computational cost decreases drastically compared to that of the other techniques. Meanwhile, the computational load of deep learning techniques is huge. Even though GRU seems suitable for HAR and may achieve satisfactory results (see previous sections), its complexity and high latency are major drawbacks. This also explains the huge computational load of CDL which not only employs a recurrent network and local handcrafted features (both proving to be effective in terms of performance), but also a convolutional one to give another dimension to the recognition process. Furthermore, it is based on a 9-DoF inertial system, which means that more information is processed by this architecture. Hence, CDL is appropriate for activity recognition. Nonetheless, it is inconvenient for embedded solutions, seeing its huge computational load and its huge power consumption (three sensors including a gyroscope are needed).

Embeddability:

The elapsed time to extract features and make a prediction is useful to evaluate the relative computational cost of the approaches. However, it does not reveal the ability of being embedded in wearable devices, seeing the limited power resources of a micro-controller.

Consequently, Appendix G shows in detail the number of operations required at each stage of As a matter of fact, if the subject is inactive, the algorithm stops at S1. Hence, the computational load is equal to 123 flops. Now, if the activity is "sitting down" for example, it reaches S3

(III-c) (transitions in Figure 3.18). Accordingly, it passes through S1 (123 flops), S2 (183 flops), and III-c at S3 (243 flops), and thus the computational complexity is 123 + 183 + 243 = 549 flops. These two paths constitute the lower and upper bounds of Ξ (computational complexity of MDA). With only few hundreds of flops, MDA is able to provide a prediction. Note that the corresponding operations (addition/subtraction, multiplication/division, multiply-and-accumulate) are done in one cycle using a hardware implementation (which is almost negligible), without any need for a software library (the case of exponential and logarithm for example).

Proof of Concept

A prototype was developed to illustrate the behavior of each HAR approach (step by step recognition) in real world situations, namely CDL and MDA. A wearable device was developed by our partner society RF-Track (Cesson-Sévigné, France). It is equipped with the inertial module LSM9DS1 featuring an accelerometer, a gyroscope and a magnetometer. I wore this device around the waist and performed a set of successive ADLs.

For the first method (involving orientation estimation) presented in section 3.3.1, the device is connected to the PC via Bluetooth dongle. Acceleration, angular velocity, and magnetic fields

Feeding Post-Processing Units

In real world conditions, a decision is made every second by the proposed HAR methods using a sliding window with L-1 L × 100% overlapping. Figure 3.22.a illustrates this operation. The illustrated signals are real acceleration data of a subject who was wearing the waist-worn device.

As shown in this figure, the subject was walking then sat down immediately (walk-to-sit). The black segments (representing successive sliding windows) were labeled as "Walking", whereas the red ones were labeled as "Sitting down". Therefore, the output is a list of predictions, as indicated in Figure 3.22.b (left array entitled Predictions). Afterwards, the labels belonging to the same activity class are regrouped and stored in an array with the corresponding indices, duration (in seconds), and status (active or inactive). For instance, suppose that L = 6 s. The first n = 11 sliding windows revealed that the subject was walking. With a prediction every second and an overlapping between two consecutive windows equal to 5 s, the corresponding duration is equal to 16 s (6 s (first window) + (n -1) × 1 s (the remaining 10 windows) = 16 s). Moreover, the status in this case is active. The same remarks hold for the remaining ADLs. Now, the postural transitions (sitting down, standing up, lying down, and rising up) are detected over several consecutive windows. Nevertheless, the transition moment only lasts for few milliseconds (around 1000-2000 ms), and thus the corresponding duration is negligible. For example, although "Sitting down" was localized in windows 12 to 15 in Figure 3.22.b, this does not mean that the subject took 9 s to sit. The red segments overlap with the black ones which contain parts of walking (see Figure 3.22.a), and thus the duration of "Sitting down" is excluded (-) so as to avoid considering some parts of the walking period twice. The same remark holds for the remaining postural transitions, i.e. the duration of these transitions is considered to be null. The re-arranged output (the right table of Figure 3.22.b) will feed post-processing units for further analysis to ensure frailty screening. Explicitly, the activity class (type of the activity), its duration, and the corresponding status will be used to compute certain activity metrics in order to assess the physical condition, as we will see in the next chapter.

In conclusion, this chapter highlighted three proposed techniques for activity recognition. The first one is dedicated to wrist-worn devices. Since this position is noisy and generates complex movements, a sophisticated approach was developed to track recurrent wrist movements. Some basic daily activity metrics, such as the number of steps and inactivity rate, can be calculated using this device. Nonetheless, this is insufficient for frailty assessment, especially that some important ADLs like sitting down and lying down are not detected. Postural transitions are not captured from this position, and thus the analysis of certain activities is not significant. Therefore, a step by step recognition process is needed to localize the successive movements of older adults for post-processing purposes. The trunk was chosen as the sensor placement for this operation due to (i) its reliability in terms of recognition and (ii) its ability to capture the posture of the human body, since it is fixed near the center of body mass. Here, two techniques were proposed. The first one is based on the orientation of the sensing unit (9-DoF inertial system) which feeds a high complexity HAR architecture, fusing three networks that are CNN, LSTM, and Dense layers. The second one is a low-cost acceleration-based approach, which divides the multinomial classification into several stages, and can be embedded in wearable devices. Researchers are invited to choose the technique that suits their application. What we learned from this chapter is that features should be extracted locally from input signals to build a robust recognition system. When computed globally, these features describe the statistical patterns of the signals, and thus increase the confusion rate between different output classes.

Sitting-down

Moreover, large feature vectors might mislead the machine and expose the model to overfitting since the learning will correspond too closely to the training set. Furthermore, recurrent networks are better suited for activity identification (even though CNN achieved relatively high results), since they learn and remember over time sequences. This is logical seeing that the activity is a sequence of movements. Additionally, the accuracy increases along with the sampling frequency F s . Nevertheless, this is not always the case for the window length L. If windows of small length L are inappropriate for the recognition, increasing this length too much can also decrease the accuracy (as it is the case of recurrent networks). Finally, dividing the multinomial classification into smaller classification tasks (the case of MDA) achieves better results, especially when dealing with lower DoFs data (accelerometer vs MARG sensor). HAR is an important tool to predict the performed activity and localize it. In the next chapter, we will see how the localized ADLs can be analyzed and associated with frailty status, and how features can be extracted to reveal the health conditions of the elderly.

The proposed eight global features are introduced hereafter:

Activity Rate: the status of the person wearing the device (active/inactive) is indicated during each activity with the corresponding duration. Suppose that d i is the duration of the i th activity (i th row of the table), thus D = i d i is the monitoring/observation period (which is equal to 86400 seconds in our case, corresponding to 24 hours). Meanwhile, D A is the sum of d i where the subject is active. The first global feature G 1 represents the activity rate and is equal to:

G 1 = D A D (4.1)
Hence, the inactivity rate is equal to 1 -G 1 . It is worth mentioning that the body posture could be identified when the subject is inactive. In fact, the postural transitions, i.e. sitting down, standing up, lying down, and rising up, are localized. Therefore, when the subject is inactive, the time during which the subject is sitting/lying can be detected. For instance, when the wearer of the waist-worn device was inactive for 15 seconds (see Figure 3.22.b), he was actually sitting since the postural transition which precedes this inactivity period is "Sitting down".

Steps: the steps are identified by peaks pk i in ||a|| (see Figure 4.1) when the subject is walking or jogging. Seeing that the MEMS accelerometer works on the principle of a mass on a spring (see Chapter 2), the spring is compressed or stretched when a step is taken. This produces a force corresponding to the acceleration (Newton's second law), which reaches a peak during this phase. Note that peaks can be detected using the method presented in section 3.2.2, or filtering methods like in [START_REF] Oliver | Mptrain: a mobile, music and physiology-based personal trainer[END_REF]. The total number of steps (over the course of the day) constitutes the second feature G 2 which is equal to:

G 2 = N i=1 pk i (4.2)
Sleep Efficiency: the system enters "night mode" between 10:00 pm and 8:00 am (the following day). Throughout this time interval, periods during which the elderly is lying are detected. A processing unit decomposes the 3 acceleration components {a X , a Y , a Z } into 5-second fragments with 80% overlapping (4 seconds). We assume that a sleep cycle consists of 5 minutes without any slight movement. The SD and range values of each component are then calculated. We call silent fragments (where the subject is not moving at all) those whose all three components Periodicity Spell: the goal here is to measure the time span of continuous walking/jogging (non-stop). It inspects the capability of elderly to reproduce periodic movements continually over long spells. Accordingly, the auto-correlation sequence of 30-second acceleration ||a|| windows 123 w i (where the elderly is active) is computed. Afterwards, the resultant sequence of M peaks P i , whose values exceed 0.3, are detected and localized. Note that the acceptable peak-to-peak separation dP i is restricted to a minimum of 200 ms. Howbeit, the output of auto-correlation must represent at least 3 peaks in order to consider the movement as periodic. Therefore, two features can be computed, namely G 4 which is the periodicity rate and G 5 which is the period T p of the periodic movements. Suppose that T is the number of windows w i which represent periodic movements, D is the monitoring/observation period in seconds, and dP i is the distance (in seconds) between the i th and the (i + 1) th peaks, hence:

G 4 = 100 × 30 × T D (4.4)
and

G 5 = 1 F s × 1 M -1 M -1 i=1 dP i (4.5)
Figure 4.1 symbolizes the relationship between this metric and the real human behavior. The period T p represents, in a certain way, the stride of human gait. For example, if a subject has a stride of length 80 cm and a period equal to 800 ms, his walking speed is equal to 0.8 0.8 = 1 m/s.

Change in Altitude: a change in atmospheric pressure P arises following three scenarios:

(i) when we use the lift, (ii) when we use the stairs, (iii) when a sudden change in temperature occurs (while opening the window or moving from one room to another one for example).

To discriminate between these behaviors, the altitude of the device is estimated every second, using Eq. (2.4), when the subject is either walking or inactive/slightly moving (like walk-tostand/stand-to-walk). The segments where the altitude is increasing or decreasing continuously that is equal to 1 if the i th activity is labeled as "stairs", and is equal to 0 if not. Consequently, two features are computed based on the change in altitude (CIA), namely G 6 and G 7 estimating the number of times the subject has used the lift and the stairs respectively:

G 6 = i 1 L (i) (4.6)
and [START_REF] Haskell | Physical activity and public health: updated recommendation for adults from the american college of sports medicine and the american heart association[END_REF], depending on their intensity. In our approach, the same logic is followed. Based on the type and the intensity of the movements, a MET value is assigned using Table 4.2. For instance, the inactivity periods, where MET is equal to 1, are localized using the HAR module with the corresponding duration (see Figure 3.22.b). For the remaining windows, i.e. when the subject is active, the type of the physical activity (cyclic/transient), its intensity (which is proportional to the SD value of the acceleration magnitude σ ||a|| ), and the corresponding time-span (duration) are known. When the subject is barely moving (light movements such as stand-to-walk for example), the corresponding MET value is equal to 1.5 if σ ||a|| is less than 0.025, and 1.8 otherwise. Now, for cyclic activity, when the subject is walking slowly (low intensity movements, σ ||a|| < 0.09), the corresponding MET is equal to 2, whereas when he is walking briskly (σ ||a|| > 0.2), the MET is equal to 5.

G 7 = i 1 S (i) (4.
Meanwhile, when he is walking moderately (i.e. 0.09 < σ ||a|| < 0.2), the MET is equal to 3.3 (see

G 8 = i C i (4.9)
Tracking the evolution of this feature might be of great importance to reveal the physical weakening of an elderly.

The proposed features will be calculated and evaluated using a wearable device placed on the body trunk (as discussed in the previous chapter), particularly waist-worn, chest-worn, and necklace devices.

Outcome in Free-living Conditions

Data of ActFreeLi were used to compute the aforementioned global features and test them in real world conditions. The study population was perfectly balanced (9 frail subjects vs 9 robust ones).

On average, participants were monitored for 31.6 (± 16.5) days, leading to a total of 570-day recordings. These subjects, ranging from 54 to 85 kg in weight and from 150 to 171 cm in height, wore the sensing device during their daily routine without any specific instruction as previously explained. Hence, each recording 24-hour file (consisting of both acceleration and barometric data) represents a typical day (daily routine) of an old person in unsupervised conditions. The proposed features G 1 to G 8 were extracted from these files, then averaged per subject, resulting in 18 values for each metric: 9 values for frail people vs 9 values for non-frail elderly. Afterwards, the mean, SD, lower and upper quartile (Q 1 & Q 3 ) of each population (i.e. of each 9 values separately) are calculated. Table 4.3 illustrates the different results. Firstly, it is clear that robust people are more dynamic, since, on average, their number of steps is significantly higher than that of frail ones (4663 vs 1019). The activity rate (in %) is another indicator. Additionally, the normalized energy expenditure (EE) (kcal/kg) decreases when people become frail, since they are less energetic and their activities involve lower intensity. This remark was mentioned in the frailty cycle developed by [START_REF] Fried | Frailty in older adults: evidence for a phenotype[END_REF]. Secondly, periodicity is hardly detectable in acquired signals of frail people. Besides, the period of this type of movement (cyclic movements) T p , which is inversely proportional to the walking speed, is significantly higher for this population compared to healthy elderly. This proves the efficiency of this feature, since a slower gait is another frailty indicator [START_REF] Fried | Frailty in older adults: evidence for a phenotype[END_REF]. Furthermore, frail people do not use the stairs except for very few situations, contrarily to the healthy ones. Anyhow, the lifestyle of robust elderly is healthier by looking at CIA features. It is worth mentioning that the distribution of body posture over the course of the day, which is linked to the inactivity rate, reveals that vulnerable subjects are mostly lying when inactive (as observed in [START_REF] Razjouyan | Wearable sensors and the assessment of frailty among vulnerable older adults: an observational cohort study[END_REF]), while robust older adults are mostly sitting. Explicitly, frail elderly spend (on average) 54% ± 12.6 of their time lying and 29.3% ± 6.5 of their time sitting. Meanwhile, robust older 24.4 28.5 * Rates are in % - † T p is in seconds - † † CIA is in times/day - ‡ EE is in kcal/kg adults spend 30.9% ± 4 of their time lying, and 41.7% ± 7.1 of their time sitting. Diversely, the variability of sleep patterns seems to be a bit lower for healthier subjects. Nevertheless, the SE looks to be subject-dependent. This feature is important when tracking the well-being of a person, but does not seem significant when discriminating between both populations. In summary, Table 4.3 allows to characterize both populations from wearable sensors point of view. Next, these measurements are discussed and interpreted using statistical and machine learning techniques, and the ability of detecting the damage in physical function is quantified.

Distribution of Data

The proposed features vary in magnitude, range, and unit. Therefore, the feature vectors should be scaled. Two models are used: a linear model, namely z-score (Eq. (4.10)), and a non-linear model, namely sigmoid (Eq. (4.11)):

(z) xi = x i -µ σ (4.10) (s) xi = 1 1 + exp(-x i -µ σ ) (4.11)
with (z) xi an element in the scaled vector using z-score, (s) xi an element in the scaled vector using sigmoid, x i an element in the original vector, µ and σ the mean value and SD of the original vector respectively.

Afterwards, Principal Component Analysis (PCA) is applied on each of the two scaled datasets to reduce the dimensionality by minimizing information loss, thus to increase the interpretability. This reduction allows us to visualize data in a 2-dimensional space in order to observe trends, jumps, clusters and outliers, and to see whether the two populations are separable using the proposed features. After applying PCA, data of both populations were plotted in a 2D space following two principal components (PCs), as illustrated in Figure 4.4. Each point represents a day, thus 295 days correspond to robust elderly and the remaining 275 days to frail people. Additionally, a kernel smoothed density was estimated and plotted for each population (top and side distributions) using the scores of the PCs. Two observations can be noted. Firstly, using sigmoid increases the discrimination power of the classification system. As seen in Figure 4.4.a (z-score), a huge overlap occurs between the side distributions (the second PC). Secondly, both populations are non-linearly separable. To confirm these observations, the boundary of SVM with Radial Basis Function (RBF) kernel is shown in both plots (dashed line). After being cross validated, the two feature vectors (PCs) fed the aforementioned classifier. The achieved balanced accuracy was 86.38% when using z-score and 93.83% when using sigmoid. Hence, for the remaining subsections, the feature vectors are scaled using Eq. (4.11).

PCA reduced the dimensionality of the dataset, by transforming the set of heterogeneous variables into a smaller one (2D) that still carries most of the information in the larger set.

Although the effectiveness of the proposed features was validated in this context, since both populations are separable as seen in Figure 4.4, this transformation done by PCA does not select the most relevant/discriminant variables. Further analysis is needed to reach this objective. displayed as small circles on the graph. Finally, the upper and lower black strips are the nonoutlier maximum (the maximum value which is not an outlier) and the non-outlier minimum respectively. The two box plots are well separated when it comes to the number of steps, the EE, the periodicity rate, the frequency of using the stairs, and the period T p . Even though the median of robust people is higher when it comes to the activity rate and the SE, there is still a significant intersection between both populations. Moreover, using the lift is irrelevant to the discrimination between the two groups of elderly. To confirm this observation, and in order to identify the relevant features, the Wilcoxon rank sum test was applied for each feature to see whether it can differentiate between robust and frail people. This test has the null hypothesis H 0 that both samples are from the same population. Table 4.4 illustrates the results, namely the p-value and whether H 0 was rejected or not (at a 5% significance level).

Identification of Discriminant Features

The results of Wilcoxon test and the box charts are coherent. The most relevant features in this context are the number of steps, the EE, the periodicity rate, the frequency of using 4.3, and the sedentary level differed significantly between both groups when computed over 48 hours [START_REF] Razjouyan | Wearable sensors and the assessment of frailty among vulnerable older adults: an observational cohort study[END_REF]. However, this information is not sufficient on a daily basis over longer periods. Finally, even though frail people sleep longer according to [START_REF] Kim | Consumer-grade wearable device for predicting frailty in canadian home care service clients: prospective observational proof-of-concept study[END_REF] (where elderly were observed for 9.43 days), the sleep patterns do not distinguish frail from non-frail elderly. Those two variables, i.e. activity rate and SE, are subject-dependent, and are not able to separate robust from frail older adults accurately. It is worth mentioning that the p-values of activity rate, SE, and Lift are 6.2%, 7.7%, and 12.8% respectively. The five most discriminant features being selected, the performance of a predictive model should be now evaluated in order to inspect its capability to detect physical weakening automatically.

Classification Process and Longitudinal Assessment

In this section, the efficiency of binary classification is presented. In other words, we assessed the capacity of the combination of the five selected features (statistically significant) to predict the health status of the person on a daily basis (since each data-point corresponds to one day). Being 4.5 illustrates the corresponding results. NN achieves the highest accuracy (93.51%) and the highest sensitivity (92.88%), which is the ability of a classifier to correctly identify frail people with a damaged physical function. GBM has the lowest false positive rate (4.73%). Hence, if we want to notify the medical staff whether the subject is becoming frail or not (on a daily basis), in order to intervene for a clinical examination, the system will send around one false alarm every 3 weeks using GBM. However, GBM is less sensitive than NN. RF is a close competitor to GBM, but with lesser specificity and sensitivity. The specificity/sensitivity trade-off should be found depending on the medical diagnosis. Now, although NN, GBM, and RF would constitute an accurate alerting system for clinicians (accuracy exceeding 91%) with a daily prediction, the false alarm rate remains somewhat high.

The frequency of diagnosis (duration between two different decisions) may affect the performance of the predictive systems. As previously discussed, the extracted measurements can be described as global features. A long-term analysis seems more suitable for such types of features. Therefore, two approaches were considered to test the performance of these three classifiers on longer periods, particularly following a 5-day prediction. For both approaches, a daily feature extraction is required. Now, regarding the first approach referred to as "Averaging", we averaged the features per 5-day (mean value of each consecutive 5 samples was computed), in a way that each sample represents the activity metric over 5 days instead of one. As for the second approach referred to as "Voting", we kept the daily prediction and we selected the most frequently occurring prediction over 5 consecutive days. For example, if the classifier predicts four negatives and one positive, then the result over those 5 days is considered to be negative. The corresponding results

for each approach are illustrated in Table 4.6. The first technique (Averaging) leads to a high specificity at the expense of the sensitivity. As we can see, the sensitivity of each classifier is below 80%. It seems that a prediction based on the average of the features over longer periods destabilizes the classifier when it comes to the identification of physical impairment. Although highly specific systems are characterized by low false positive rates (and thus fewer number of false alarms), the ability to detect physical weakening is somewhat low in this case. The voting technique, contrarily to the averaging one, raises both the sensitivity and the specificity. The latter rose up to 98.08% for the three classifiers, meaning that one false alarm is generated every 8-9 months. Additionally, the sensitivity of NN is 98.25%, which makes it a reliable solution for this task. These results highlight the importance of targeting a longitudinal study for such type of measurement. For worsening detection, a daily feature extraction with a daily prediction should be done. However, the final decision should be based on the most frequently occurring prediction over longer intervals (5 days for example), in order to notify or not the authorized team about a possible physical weakening. In other words, with a 5-day decision, a notification/alarm is sent once per 5 days based on the previous 5 predictions (done on a daily basis). Features like the number of steps and EE for instance possess high variability over small periods, i.e. they may differ considerably between consecutive days. This justifies the high performance, particularly for NN, when a longitudinal assessment was targeted. Figure 4.6 illustrates the performance of NN as a function of time (in days), using the voting technique. The evaluation measures are improved when longer periods are considered, until we reach 100% for a weekly assessment.

Gait Analysis

Chapter 1 has shown that the gait velocity has been a talking point in the past decades. Nonetheless, walking is a complex activity of daily routine and cannot be restricted to one variable. Other features may vary during the transition towards frailty. Moreover, the walking speed (in m/s) cannot be measured accurately with an accelerometer, but with a chronometer. An approximation (T p ) was introduced in the previous section. Accordingly, other gait parameters are proposed and associated with frailty status. Seeing that the walking periods are localized, thanks to the HAR techniques previously described in chapter

Feature Extraction

The target is the extraction of handcrafted features from acceleration, describing the gait of the elderly in regards to frailty status. Two components are considered in this analysis, namely the acceleration magnitude ||a|| and the vertical component a X . It is worth noting that when the wearer of the device is walking, the vertical component is the combination of both (i) the static acceleration of the Earth gravity (1 g) and (ii) the dynamic acceleration caused by the body (a X oscillates around 1 g).

F 1 = max( ||a||) -min( ||a||) (4.12)
Trimmed estimators were discussed in the literature [START_REF] Stigler | Do robust estimators work with real data[END_REF][START_REF] Wilcox | Introduction to robust estimation and hypothesis testing[END_REF]. Their use helps to eliminate the influence of outliers. This feature quantifies the intensity of movements related to the gait.

𝐹 1 = 0.43 𝑔 𝐹 1 = 0.17 𝑔 𝐹 Feature F 3 : since walking is a cyclic activity, the periodicity of the acceleration signal is one of the cornerstones of gait analysis. Here, the goal is the observation of similarity between the acceleration magnitude and its delayed version as a function of time lag τ , to verify the presence of cycles in the signal. Consequently, the auto-correlation A(τ ) is computed following three steps [START_REF] Box | Time series analysis: forecasting and control (3rd)[END_REF]:

1 = 0.09 𝑔 𝐹 2 = 2 𝑠𝑡𝑒𝑝𝑠/𝑠 𝐹 2 = 1.33 𝑠𝑡𝑒𝑝/𝑠 𝐹 2 = 1 𝑠𝑡𝑒𝑝/𝑠 Robust Pre-frail Frail (a) (b)
                 F R (f ) = F{|| a||} M (f ) = ||F R (f )|| 2 F R (τ ) = F -1 {M (f )} A(τ ) = Re{F R (τ )}
where || a|| denotes the demeaned acceleration magnitude, F is the fast Fourier transform, F -1 its inverse, and Re{X} the real part of X.

A(τ ) is then normalized, by dividing its components by A(0) (its maximum value).

F 3 = log(W ) - 10 i=1 t i T log( t i T ) (4.14)
Feature F 4 : the dynamism of the elderly while walking might be an important indicator of frailty. To this end, we could monitor the sudden jumps in the acceleration magnitude ||a|| during gait periods, which reflect, in some way, the variability of the time-series. The goal behind this fourth feature is to count the number S of times where the absolute value of the difference between two consecutive acceleration samples exceeds a predefined threshold found by trial and error (in our case equal to 0.075 g). The total count is then divided by the number N of samples in the signal. This feature F 4 is inspired by a widely used measure of heart rate variability, namely the pNNx [START_REF] Mietus | The pnnx files: reexamining a widely used heart rate variability measure[END_REF]:

F 4 = S N (4.15)
Features F 5 & F 6 : here, the vertical component a X is concerned. A fitted AutoRegressive model (AR) to the time-series could be relevant in gait analysis to detect physical weakening.

This model predicts the future behavior based on the past. The time-series X t (representing the vertical component) is explained linearly by its past values X t-i , a bias b, and a stochastic term t [START_REF] Neumaier | Estimation of parameters and eigenmodes of multivariate autoregressive models[END_REF]:

X t = b + p i=1 φ i X t-i + t (4.16)
p is the order of the model and φ i are its parameters. Note that φ i is the i th element of φ.

Eight AR models are estimated [START_REF] Schneider | Algorithme 808: arfit-a matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models[END_REF], from order 1 to order M (p = 1, ..., M , with M equal to 8 in our case). Afterwards, two criteria are applied to choose the optimal order p, namely Akaike information criterion (AIC) or Bayesian information criterion (BIC). The smallest value for this order is selected. For example, when an AR model of order p = 3 is fitted, φ 4,...,M are set to 0. Then, two features are calculated to encode the set of AR model parameters. Feature F 5 is the standard deviation σ φ of vector φ (parameters of AR model):

F 5 = 1 p p i=1 (φ i -µ φ ) 2 (4.17)
where µ φ is the mean value of φ.

Feature F 6 is the kurtosis K φ of vector φ, indicating whether the distribution of the AR model parameters (set of parameters φ i ) is tight (smaller AR order) or flattened (higher AR order):

F 6 = 1 M M i=1 (φ i -µ φ ) 4 [ 1 M M i=1 (φ i -µ φ ) 2 ] 2 (4.18)
Expressly, it identifies whether the tails of this distribution carry some extreme values or not.

Outcome in Free-living Conditions

In addition to the recruited subjects of ActFreeLi, acquired data in WWBS Metrics public dataset [START_REF] Orselli | Wwbs metrics[END_REF] from FrailSafe project were added. A sensorized smart-vest garment (FrailSafe, 2017) was developed by SMARTEX, and was equipped with an IMU placed on the chest. Data were acquired in free-living conditions during elderly's daily routine. Therefore, acceleration signals were processed to localize gait periods. Since walking periods vary from one subject to another, the corresponding signals were cut using 6-second windows. This length (6 s) is appropriate for this task, since the proposed system operates automatically in unsupervised conditions. While shorter windows may discount some descriptive parts of the gait cycles, larger windows may contain some movements of a different activity, especially when the target is the analysis of the senior's gait in his daily routine.

The aforementioned six features were extracted from these windows. They represent the way the elderly person walks. Figure 4.8 illustrates the violin plots corresponding to the proposed gait parameters. According to this figure, the first four features, i.e. the movements intensity (trimmed range), the cadence (steps/s), the periodicity (distribution entropy of the auto-correlation signal), and the variability (pNN) are monotonic. The median of the first class (Robust) is the highest, and decreases when the subject is pre-frail and even more when he is frail. Now, when it comes to feature F 5 , the median increases during the transition from robust to pre-frail and then decreases from pre-frail to frail. For feature F 6 , the opposite behavior is observed, i.e. the median decreases then increases during the transition between the different frailty classes. Regarding the cadence, let us indicate that it is one of the temporospatial features that were proposed in the literature [START_REF] Kressig | Temporal and spatial features of gait in older adults transitioning to frailty[END_REF][START_REF] Montero-Odasso | Gait variability is associated with frailty in community-dwelling older adults[END_REF]. Under supervised conditions, the cadence of very fit/healthy elderly is around 1.86 ± 0.14, whereas that of the "transitioning to frailty" older adults is around 1.76 ± 0.21 steps/s respectively [START_REF] Kressig | Temporal and spatial features of gait in older adults transitioning to frailty[END_REF][START_REF] Winter | Biomechanical walking pattern changes in the fit and healthy elderly[END_REF]. Interestingly, the proposed feature F 2 shows that this variable is around 1.67 ± 0.18 steps/s for robust people, 1.33 ± 0.23 steps/s for pre-frail elderly, and 1 ± 0.43 for frail older adults, when calculated over 6 seconds using a wearable accelerometer in free-living conditions. The individual performance of each feature has then been studied, using (i) the NB classifier with 10-fold cross-validation (3-class classification) and (ii) Kruskal-Wallis test, which is an extension of Mann-Whitney U test. Hence, the performance has been quantified by the balanced accuracy and the p-value at 1% significance level. Table 4.7 illustrates these two quantities for each feature. The gait parameters are statistically significant (p-value < 1%).

Moreover, the balanced accuracy ranges from 58.1% to 73.2%. These results show that the proposed features are good indicators for frailty, but are not sufficient individually to discriminate between these three classes, seeing the existence of some overlapping between the violin plots of different classes and the relatively small balanced accuracy values.

Classification Process and Physical Condition

The next objective is to combine the proposed six gait parameters into one feature vector and to apply a machine learning classifier to stratify elderly into three classes, namely robust, pre- 4.11)). As seen in the previous section, the values are scaled between [0, 1], while the distribution in the new 6D space is modified, since the model is nonlinear. This might help to separate the three clusters (three classes) in the 6D space in order to increase the accuracy of the predictive model. PCA was applied to the scaled feature vectors in order to reduce the dimensionality and plot data in a 3D space, as illustrated in Figure 4.9. Three clusters can be observed: the first one (blue points) with a (0.33; -0.03; 0.01) centroid represents the robust population, the second one (yellow points) with a (-0.13; 0.36; 0) centroid represents the pre-frail population, and the third one (orange points) with a (-0.47; -0.18; 0) centroid represents the frail population. A certain intersection can be seen between each pair of clusters. Here again, i.e. from gait analysis point of view, the different populations are non-linearly separable. Now, LSO cross-validation was applied to evaluate the discrimination power of the proposed parameters. The considered classifiers are (1) NN with one hidden layer of 15 neurons, using a logistic activation function, (2-3) SVM with two kernels, namely quadratic (SVM Q ) and RBF (SVM R ), ( 4) KNN with k = 5, (5) DT with a depth equal to 10, (6) RF of 10 estimators and a depth equal to 10, and (7) GBM of 100 estimators, a maximum depth equal to 5, and a learning rate equal to 0.1. Table 4.8 illustrates the different results (in terms of accuracy) of the aforementioned classifiers. The accuracy ranges from 85.42% to 88.5%. With a 88.5% accuracy, SVM R is the top performer, followed by NN (88.18%) and GBM (87.51%). Now, it is worth mentioning that the number of estimators n of RF is relatively small, compared for example to GBM which uses already 100 estimators. Increasing n might stabilize RF and increase its accuracy. Therefore, we inspected the performance of RF in terms of accuracy (%) as a function of n as illustrated in frail. Furthermore, 8.4% of signals labeled as frail were classified as pre-frail by SVM R . Now, at first sight, the attained accuracy of 88.5% could be seen as an underachievement.

However, the previous result means that, based solely on the proposed six gait variables, one can predict the frailty status with an accuracy around 88-89%. We should keep in mind that the frailty syndrome is much more than the gait analysis, and the ground truth is based on 5 different indicators. For example, a subject with a good gait quality could be evaluated as pre-frail due to an unintentional weight loss and/or weak grip strength. Therefore, the achieved accuracy has its limits; thus, the 88.5% accuracy is quite satisfying. Furthermore, the classification is a "frozen" process in this context, i.e. the prediction is done at a particular time (a specific day). However, the evolution of those parameters with respect to the frailty curve and the long-term surveillance are what matter most. The goal is to understand what happens to the gait during the transition from one cluster to another (Robust → Pre-frail or Pre-frail → Frail) in the 6D space. This is far more relevant than a classification performance, and the proposed model is a relevant tool to answer this question. It is worth mentioning that due to several lockdowns and social distancing that were imposed due to the covid-19 pandemic, some robust participants were classified as pre-frail by FrP. In fact, the exhaustion criterion of FrP (see Appendix A) was satisfied for those subjects, whose psychological state was affected during this period. When the situation got better and these restrictions were lifted, these older adults got better and became robust again according to FrP. Nonetheless, their gait has been only slightly little affected during this phase, even if FrP suggested a certain physical weakening.

Archetype for Monitoring Systems

The proposed features -the global features as well as the gait parameters -have proven to be good indicators when it comes to the detection of physical worsening and the separation of frail from non-frail elderly. In case of a physical damage, the system can notify the medical staff and/or the family members. To this end, with a view for a marketable product, we might consider either (i) a highly sensitive system, which sends a notification if one of the two types of features (global or local) suggests physical weakening, or (ii) a specific system that sends a notification only if both types of features suggest physical worsening. It is worth mentioning that the first choice might generate a fairly large number of false alarms. Alternatively, the false alarm rate should decrease when it comes to the specific system but at the expense of the sensitivity. This choice depends on the users of the system and the desired trade-off between specificity and sensitivity. Now, the main purpose of this monitoring system is to assist the clinician when dealing with frailty. Sending alarms in case of a physical weakening is insufficient for frailty assessment due to the complexity of this syndrome. The clinician has to understand what makes the system send these alarms, and needs to appreciate the evolution of the activity metrics and indicators to conclude his examination. Therefore, a graphical representation of these features is now proposed for a better interpretation. The idea here is to offer a tool whose output resembles a daily report consisting of values and illustrations to improve the diagnosis. Figure 4.12 illustrates the output. This report begins by providing the distribution of activity (activity rate per hour) over the course of a day, using the blue bars in the first graph of the figure. This feature is important, and represents an overview regarding the behavior of elderly. For example, the corresponding subject is highly active between 9 am and 12 pm. He is mostly inactive at night (while he is sleeping). Even if the activity rate has been shown to be statistically insignificant to distinguish robust from frail subjects (see section 4.1.4) the distribution of this variable over time might reveal a certain routine that is associated with the health conditions of the older person. Along with the activity rate, the number of steps and EE in kcal are two other variables illustrated in this report. Afterwards, the sleep efficiency is also mentioned, while showing the sleep patterns.

As seen in Figure 4.12, the sleep cycles are pictured in green triangles, and the interruptions in red rectangles. The bigger the area of the triangle/rectangle, the longer the period of the sleep cycle/interruption. Two types of interruptions are detected: (i) small ones resulting from rotation or change of positions, and (ii) relatively longer ones resulting from higher activity levels, where the subject is active and moving. The latter is represented by the second and fourth interruptions in the report, when the subject woke up and walked. This result is coherent with the activity rate diagram (blue bars), where it is shown that the subject was active between 1-2 am, and 4-5 am. Then he went into deep sleep again, since the fifth cycle is large. This seems a good indicator, showing that the subject has no sleep perturbation even when he wakes up at night. Although the sleep efficiency is not able to distinguish frail older adults from robust ones, the evolution of the sleep patterns over time might reveal some important clues to the frailty trajectory, seeing that this feature is subject-dependent. Furthermore, the ability of performing periodic movements (PMVs) and gestures (particularly continuous walking and/or jogging) is clearly displayed. First, the distribution of these movements is illustrated (the rate per hour) using dark orange bars. In our case, 60% of the subject's movements were periodic between 10 am and 11 am. It seems that this older adult was walking continuously at this particular time. However, between 11 am and 12 pm, only 3.3% of the activities are periodic. This graph gives another dimension to the diagnosis. As a matter of fact, the subject was more active at [9 -10] am than at [10 -11] am according to the first graph (activity rate). Nonetheless, the periodicity was hardly detectable before 10 am. In addition, the PMVs cycles are also calculated using yellow bars. Even though the periodicity rate was high between 10 am and 11 am, the PMVs never exceeded 25 minutes. Explicitly, the subject performed eleven periodic cycles that lasted between 0 and 5 minutes, one periodic activity that lasted between 5 and 10 minutes, and another periodic cycle between 20 and 25 minutes. Finally, the barometric features are also an important factor to be monitored. They are portrayed by the number of times the subject has used the lift and/or stairs, as mentioned at the end of the report. The clinician can easily assess the quality of life of the old person, and how many times a change in environments occurs. Here, the subject took the lift upward for 2 floors at 7:44 pm. He descended the stairs at 12:13 pm.

In this solution, 3 meters correspond to one floor. The number of times the older person has used the stairs is a robust indicator to frailty. However, the statistical significance is non-existent when it comes to the lift. Nevertheless, this information is essential for health monitoring of old people, especially if the person is living alone. It reveals whether this person is autonomous and independent or not, and if she can go out regularly (for a walk/leisure activity for example). Now, with the proposed monitoring system, the history of the extracted activity features could be shown in order to track their evolution and define the frailty trajectory. Figure 4.13 illustrates an example of two global features. The number of steps and the activity rate are calculated on a daily basis and these two graphs show the corresponding values over the last 6 days. Globally, the older adult whose metrics are illustrated in this figure is healthy and quite active. On average, he took 3662.5 steps per day between September 22 nd and September 27 th . Nonetheless, on September 24 th , the number of steps was relatively low (1562) and the inactivity rate was considerably high (83.4%). Hence, a false alarm would be sent on that day with a daily prediction, since the values of activity features dropped and thus suggest a potential physical weakening. This justifies once again the importance and the need of a longitudinal study for frailty analysis when it comes to global features.

Finally, the gait periods could also be shown, as illustrated in (corresponding to a gait period), the gait parameters appear. In our case, when the subject was walking between 02:52 pm and 02:53 pm, the related features (calculated using the aforementioned technique) like the intensity of the movement, the cadence, and the stride appear on the screen with the corresponding frailty status.

These parameters are linked to the occurrence of an outcome of interest, like a certain disease and its association with risk factors. Progressive weakening justifies the need of a continuous monitoring. This tool assists the clinical expert and can help him in his diagnosis since it makes him able to observe the evolution of these parameters and to receive alarms in case of physical worsening, in order to intervene and help elderly living independently. This prototype, which is a handy tool, is an answer to overcome the different problems of frailty.

In conclusion, this chapter focused on the analysis of ADLs after their identification by by applying a set of machine learning classifiers in order to detect physical worsening of elderly and separate frail subjects from robust ones. Our analysis showed that a longitudinal study is important while using global features, to ensure a highly accurate diagnosis. The idea is to extract these variables and predict the elderly status on a daily basis, then notify the authorized team once every 5 days or once a week (depending on the application), by selecting the most frequently occurring prediction. Besides, gait parameters were also proposed. Here, a cross-sectional study was adopted, since the physical condition was estimated by analyzing six gait parameters at a particular moment. Here again, the statistical significance of each feature was evaluated and the discrimination power of a predictive system was discussed based on these six variables. In a future work, the user might choose a highly sensitive system, which sends a notification if one of the two types of features (global or local features) suggests physical weakening, enduring a relatively high false alarm rate. Alternatively, he might prefer a specific system, which sends a notification only if both types of features suggest physical worsening. The model depends on the application and its users. In addition to the alerting system, a tool was proposed which exploits the estimated measurements of both modules (HAR and ADLs analysis) and represents them graphically for a better interpretation. This tool is an added value to the monitoring system, since the evolution of health and activity features is important to define the frailty trajectory of a person, especially that some variables were shown to be subject-dependent, and thus their progression over time may suggest physical weakening in case the alerting system fails to detect it. The proposed system as a whole (from data acquisition to activity recognition and analysis) outperforms traditional performance tests and clinical assessments. The activity monitoring and the evaluation of physical condition are done automatically in unsupervised conditions over long periods, which increases the accuracy of the diagnosis and constitutes the basis for future preventive systems.

CONCLUSION

Our research mainly focused on activity monitoring of older adults to evaluate frailty conditions in unsupervised conditions. As seen at the beginning of this thesis, frailty would affect more than 70% of people over 85 years old. This geriatric syndrome leads to physiological weakening and adverse outcomes like hospitalization, lack of autonomy, and even death. In order to attenuate physical worsening and interrupt the transition towards disability, a punctual medical intervention is needed. As life expectancy is increasing worldwide, the prevalence of frailty is rising rapidly. This justifies why we can see a growing necessity to concentrate on research and development of efficient approaches to take on this challenge.

With the absence of a gold standard, several attempts have been made to detect the frailty status. A set of performance tests and questionnaires have been developed, like SPPB, TUG, and DGI to name a few, as well as the measurement of clinical and self-reported data (the case of FrP and FrI), to assess the physical condition of elderly. As discussed earlier, these tests and questionnaires are conducted in supervised conditions, which eliminates the notion of early detection and automatic diagnosis. Additionally, the use of subjective measures is not accurate enough, and might be sensitive to the conditions of the subject, such as the mental and sentimental states. Furthermore, FrP and FrI detect the current state of elderly, but are not efficient when it comes to the detection of progressive weakening. Biomarkers have been also considered in the literature, but their relationship to frailty is unclear to date, and thus they do not satisfy frailty screening. Therefore, the development of monitoring systems, based on connected devices, is perfectly adequate in this context. Now, wearable devices are preferred to ambient sensors for various reasons. The former type does not reveal the identity of the wearer and accompanies the older adult almost everywhere.

Wearable sensors are capable of continuously collecting data and permanently monitoring the health conditions of people during their daily routine. This is not the case of external sensors like cameras, which also suffer from diversity in camera views and visibility issues. They are also shortened to certain environments, and have their limitations linked to the variety of subjects.

Therefore, the goal is to detect the human movements and activities continuously, by developing a step by step recognition approach which predicts the performed activity instantaneously. The role of this HAR module is the detection and time localization of ADLs based on acquired data. Once the ADLs are localized, a second module is responsible for activity analysis. In other words, informative activity metrics are extracted from segmented and labeled windows in order to assess the health conditions of the subject and detect the frailty status. The system provides a summary regarding the extracted variables which characterize the physical function, as well as their evolution over time, and can send a notification to the authorized team and family members in case of a physical worsening.

Throughout this thesis, the contributions of this work were explained and justified using scientific interpretation and/or experiments and can be summarized as follows:

• Review of different monitoring methodological tools, in order to choose the components of our system. It was seen that MEMS are preferred to PEC systems in this context, and that acceleration-based solutions outperform other methods in terms of power consumption.

Moreover, the trunk was chosen as the most suitable position based on several factors.

Furthermore, the computational complexity of classifiers was calculated to get an idea regarding embedded algorithms.

• Design of FallAllD dataset to develop HAR techniques, consisting of a wide set of human falls and ADLs. Based on the limitations of state-of-the-art datasets, a comprehensive experimental protocol was adopted to collect data using four different sensors, namely accelerometer, gyroscope, magnetometer, and barometer. Different scenarios were considered for the activity, like walking with different speeds (slowly and quickly), cautious and normal sitting down (stand-to-sit and walk-to-sit) to name a few. High sampling frequencies were chosen for data-loggers in order to study the effect of this variable on the reliability of the monitoring system.

• Design of ActFreeLi dataset which is dedicated to frailty analysis. It consists of older adults' movements in free-living conditions during their daily routine. The participants were visited several times to assess their physical condition and their psycho-cognitive health during the monitoring period.

• Proposal of a sophisticated solution for wrist-worn trackers in a first instance, which targets cyclic ADLs and inactivity periods. The goal was to localize cyclic activities as well as resting/inactivity periods, in order to calculate some activity metrics (such as the number of steps and activity rate). Even if this wrist-worn device outperforms other trackers in terms of acceptability, and may accompany elderly everywhere, this solution is insufficient for a comprehensive frailty analysis. Firstly, the position of the device is not able to capture postural transitions. Additionally, and seeing that the arm moves with high DOFs, the reliability of this device in free-living conditions is questionable. Therefore, the remaining contributions focused on the trunk-placed trackers.

• Proposal of a high complexity HAR approach based on a MARG sensor (placed on the trunk). A sensor fusion technique, namely Madgwick's algorithm, estimates Euler angles using signals acquired by an accelerometer, a gyroscope, and a magnetometer. A novel feature fusion architecture, consisting of CNN, LSTM, and Dense layers, was developed to process the estimated angles as well as acceleration signals. The outputs of these networks are concatenated to predict the activity represented by the windowed data. Experimental results showed the effectiveness of this approach.

• Proposal of a low-cost acceleration-based HAR technique (the sensor being placed on the trunk). Feature vectors, computed in parallel with data acquisition using an efficient online feature computation technique, encode the temporal structure of acceleration patterns since they are extracted locally. These vectors feed a novel classification model called MDA, which divides the multinomial classification into three stages to predict the activity.

Experimental results on five public datasets demonstrated that this method (i) is highly accurate, (ii) avoids overfitting, and (iii) requires low computational load.

• Proposal of global features, extracted over the course of the day, in order to characterize the physical function of older adults. This set of heterogeneous features was first extracted from acquired data during daily routine in free-living conditions. Next, these measurements were analyzed to select the most relevant features in the context of frailty. The discrimination power of the selected subset was also investigated using machine learning models. It was seen that both populations, namely frail and non-frail elderly, can be separated using nonlinear boundary. Furthermore, with this type of features, a longitudinal study is needed to obtain a highly accurate system.

• Development of a gait analysis module to study the relationship between the way the elderly walks and his physical condition. Six gait parameters were proposed and tested on several machine learning models. The proposed gait analysis is able to separate robust, prefrail, and frail populations to some extent. These variables were shown to be statistically significant. It was also observed that the confusion between the different output classes could be considered as useful clues in the analysis of the frailty trajectory.

• Design of a paradigm for monitoring systems, outlining the physical condition of elderly in exhaustive detail. Based on a graphical representation, the developed system is able to provide a daily report displaying the calculated metrics (using charts), their evolution over time, as well as the occurrence of certain ADLs over time (date, time, duration). The goal of these attributes is to assist the clinician during his diagnosis.

Future work of this project would mainly focus on four points to extend the present work:

• Firstly, the developed techniques could be tested on wider sets to fine-tune the parameters and increase the reliability of the system. Hence, the models have to be evaluated on a larger dataset composed by older adults of diverse profiles, which ensures the generalization of machine learning techniques, i.e. the capability to forecast unseen data. Moreover, since data acquisition (in free-living conditions) will be pursued until the end of August 2022, this

gives us the opportunity to study the corresponding frailty trajectories of the participants.

For instance, we have seen in the previous chapter that the number of steps decreases when the subject tends to become frail. Nonetheless, we still do not know whether this feature decreases linearly, exponentially or in another way, during the transition towards frailty.

The same remark holds for the remaining features.

• Secondly, the psycho-cognitive health could be considered when evaluating the frailty con- • Thirdly, the frailty status could be assessed by combining (1) clinical data such as weight, blood pressure, and heart rate, (2) physical activity-related data (the proposed features in Chapter 4), and (3) psycho-cognitive health-related data (texts representing the speech of older adults). Consequently, a multimodal system could be created to ensure frailty screening. This system would consist of the aforementioned main axes, whose inputs are categorical data, time-series (acquired by wearable sensors), and texts respectively. The output of those axes will be fused for a better knowledge of the physical condition. Although the physical function is a great indicator to frailty, we might need the two other axes (clinical/physiological data and psycho-cognitive health) for an accurate early detection and a better preventive system.

• Fourthly, the ability to predict future physical worsening over different time scales could be investigated. A score of (a) 0 criterion means that the person is robust or not frail, (b) 1 or 2 criteria means that the person is pre-frail, (c) 3-5 criteria indicates that the person is frail.

Short Physical Performance Battery (SPPB)

Short Physical Performance Battery consists of three tests as explained in [START_REF] Guralnik | A short physical performance battery assessing lower extremity function: association with self-reported disability and prediction of mortality and nursing home admission[END_REF]):

• Balance tests: the participant must be able to stand unassisted, without the use of a cane or walker, following three positions.

Position Score

Site-by-side "1" if held for 10 seconds, "0" otherwise Semi-tandem "1" if held for 10 seconds, "0" otherwise Tandem "2" if held for 10 seconds, "1" if held for 3 to 9.99 seconds, "0" otherwise

Pittsburgh Sleep Quality Index (PSQI)

The subject has to answer a set of questions as indicated in [START_REF] Buysse | The pittsburgh sleep quality index: a new instrument for psychiatric practice and research[END_REF]. Answer: "0" not during the past month, "1" less than once a week, "2" once or twice per week, "3" three or more times a week.

6. During the past month, how often have you taken medicine to help you sleep (prescribed or "over the counter")?

Answer: "0" not during the past month, "1" less than once a week, "2" once or twice per week, "3" three or more times a week.

7. During the past month, how often have you had trouble staying awake while driving, eating meals, or engaging in social activity?

Answer: "0" not during the past month, "1" less than once a week, "2" once or twice per week, "3" three or more times a week.

8. During the past month, how much of a problem has it been for you to keep up enough enthusiasm to get things done?

Answer: "0" no problem at all, "1" only a very slight problem, "2" somewhat of a problem, "3" a very big problem. 9. During the past month, how would you rate your sleep quality overall?

Answer: "0" very good, "1" fairly good, "2" fairly bad, "3" very bad.

Seven components are derived, each scored 0 (no difficulty) to 3 (severe difficulty). The components are summed to calculate a global score (range from 0 to 21). Higher scores mean worse sleep quality.

• Component 1 -Subjective sleep quality: response to question 9

• Component 2 -Sleep latency: response to question 2 ("0" ≤ 15 minutes, "1" 16-30 minutes. "2" 31-60 minutes, "3" > 60 minutes) + response to question 5.a.

• Component 3 -Sleep duration: response to question 4 ("0" > 7 hours, "1" 6-7 hours, "2" 5-6 hours, "3" < 5 hours)

• Component 4 -Sleep efficiency: Sleep efficiency (SE) = hours slept (question 4)/hours in bed (questions 1 & 3). The score of this component is the following: "0" if SE > 0.85, "1" if SE = 0.75-0.84, "2" if SE = 0.65-0.74, "3" if SE < 0.65.

• Component 5 -Sleep disturbance: S C5 is the sum of responses to questions 5.b to 5.j.

The score of this component is the following: "0" if S C5 = 0, "1" if S C5 = 1-9, "2" if S C5 = 10-18, "3" if S C5 = 19-27.

• Component 6 -Use of sleep medication: response to question 6.

• Component 7 -Daytime dysfunction: S C7 is the sum of responses to questions 7 to 8. The score of this component is the following: "0" if S C5 = 0, "1" if S C5 = 1-2, "2" if S C5 = 3-4, "3" if S C5 = 5-6.

orientation D E q of a frame E relative to frame D is done through a rotation of angle θ around an axis d defined in D: D E q = [q 1 q 2 q 3 q 4 ] (B.2) ϑ D and ϑ E are the description of the vector ϑ as a pure quaternion in frame D and frame E respectively, i.e. a value of 0 is inserted as a first element to make it a quaternion. Based on the previous remarks, the 3D rotation is ensured using the following equation: [START_REF] Kuipers | Quaternions and rotation sequences: a primer with applications to orbits, aerospace and virtual reality[END_REF][START_REF] Madgwick | An efficient orientation filter for inertial and inertial / magnetic sensor arrays[END_REF]:

ϑ E = D E q ⊗ ϑ D ⊗ D E q (B.
           ψ = Atan2(2q 2 q 3 -2q 1 q 4 , 2q 2 1 + 2q 2 2 -1)
θ = -sin -1 (2q 2 q 4 + 2q 1 q 3 ) φ = Atan2(2q 3 q 4 -2q 1 q 2 , 2q 2 1 + 2q Assuming that k m 0 = w 0 , the general solution is:

x(t) = C 1 cos (w 0 t) + C 2 sin (w 0 t) (E.

3)

The mass was released from the equilibrium point (x(0) = C 1 = 0):

x(t) = x 0 sin (w 0 t) , x 0 < 0 (E.4)

By replacing x(t) in (E.1) by its value in (E.4), we get: a(t) ∼ a 0 sin (w 0 t) , a 0 > 0 (E.5)

Note that for "sitting down", we get the same acceleration with an opposite sinusoidal function. nal, vol. 20, no. 20, pp. 12384-12395, Oct. 2020. → doi: 10.1109/JSEN.2020.3000394 International Conferences

BIBLIOGRAPHY

Figure 1 -

 1 Figure 1 -Diagramme illustrant les différents éléments du projet ACCORDS.

Figure 3 -Figure 4 -Figure 5 -

 345 Figure 3 -Signaux d'accélération résultant de quatre classes, mesurés à l'aide d'un accéléromètre porté au poignet.

Figure 7 -

 7 Figure 7 -Architecture proposée de la technique de classification, composée de deux réseaux de Deep Learning (CNN et LSTM) et d'un réseau de neurones entièrement connecté (Dense).

Figure 8 -Figure 9 -

 89 Figure 8 -Algorithme de décomposition multinomiale proposé, composé de trois étapes S1 → S3, qui prédit l'activité réalisée à faible coût de calcul.

Figure 10 -

 10 Figure 10 -Signaux de marche. (a) Module de l'accélération ||a|| représentant la marche de chaque population (les pas étant représentés par des cercles rouges) et (b) coefficients d'autocorrélation correspondants.

3. 18

 18 Proposed multinomial decomposition algorithm, consisting of three stages S1 → S3, which predicts the performed activity at a low-cost. . . . . . . . . . . . . . . 107 3.19 Heatmap consisting of the achieved accuracy (%) for each (F s , L) pair after applying MDA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 3.20 Performance of MDA in terms of precision and recall for each targeted activity using 1-vs-all strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 3.21 The achieved accuracy (%) when (i) F s is fixed and L is variable (left graph) and (ii) L is fixed and F s is variable (right graph). . . . . . . . . . . . . . . . . . . . . 112 3.22 Output of HAR module. (a) The step by step recognition using a sliding window with overlapping. (b) The raw output of HAR technique (list of decisions) and its transformation into an array summarizing the succession of performed ADLs with the indices of the sliding windows, the corresponding duration (in seconds), and status (active/inactive). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.1 Human behavior vs acceleration magnitude ||a|| while walking (recurrent movements). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.2 Magnitude ||a|| of two signals with the same SD value. . . . . . . . . . . . . . . . 124 4.3 Change in altitude while using stairs (tan(θ S ) ≈ 0.23m/s) and while using the lift (tan(θ L ) ≈ -0.66m/s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.4 Data distribution of both populations following two components, with the SVM boundary in dashed lines, after being scaled using (a) z-score formula and (b) sigmoidal function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.5 Box charts showing the data distribution of each feature (x-axis) for both populations (Robust vs Frail). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 4.6 Performance of NN (using the voting technique) as a function of time (in days) in terms of Sensitivity (Sen), Specificity (Spe), and Accuracy (Acc). . . . . . . . 134 4.7 Gait signals. (a) Acceleration magnitude ||a|| representing the gait of each population (steps in red circles) and (b) the auto-correlation values as a function of a lag τ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 4.8 Violin plots of the proposed gait parameters. Features F 1 to F 4 , which are extracted from ||a||, represent the movements intensity, the cadence, the periodicity, and the variability of the gait respectively. Features F 5 and F 6 , which are extracted from a X , represent the time-varying process through the SD and kurtosis of the AR model coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 4.9 Data distribution of the three populations following three principal components pc 1 , ..., pc 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4.10 Accuracy (%) of RF as a function of the number of estimators n. . . . . . . . . . 142 4.11 Confusion Matrix resulting from SVM with a RBF kernel (SVM R ). . . . . . . . . 143 4.12 An example of a daily report illustrating real data of an old person in free-living conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.13 History of two activity metrics (steps and activity rate) on a daily basis over the past week. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.14 History of gait periods in a specific day with the corresponding time and duration. The corresponding gait parameters and the predicted frailty status appear on the screen when the user selects a cell. . . . . . . . . . . . . . . . . . . . . . . . . . . A.1 Feet positions for SPPB balance test. . . . . . . . . . . . . . . . . . . . . . . . . . E.1 A simplified model of a MEMS accelerometer. . . . . . . . . . . . . . . . . . . . . F.1 Hyperbolic tangent sigmoid (blue) vs customized function (orange). . . . . . . .

Figure 1 -

 1 Figure 1 -Flow diagram illustrating the elements of ACCORDS project.

Figure 1

 1 Figure 1.1 -The different stages of frailty model with aging curves as a function of age, namely normal aging and accelerated aging.

Figure 1 . 3 -

 13 Figure 1.3 -Biomarkers for frailty screening and analysis.

Figure 1 . 4 -

 14 Figure 1.4 -The three components (a X , a Y , a Z ) of an acceleration signal representing the different phases of a forward fall while walking caused by a slip.

Figure 1

 1 Figure 1.6 -Flow diagram of the present work, where activity monitoring is divided into three main steps.

Figure 2 .

 2 Figure 2.1 -Accelerometers vs Gyroscopes in terms of consumed current (extracted from (Q. Liu et al., 2017)).

Figure 2 . 2 -

 22 Figure 2.2 -Recordings of acceleration signals acquired from six different body locations (extracted from (Cleland et al., 2013)).

Figure 2 . 3 -

 23 Figure 2.3 -Recordings of acceleration signals resulting from four activities, using a wrist-worn accelerometer.

Figure 2 . 4 -

 24 Figure 2.4 -The barometric pressure as (i) raw signal (green), (ii) slope-limited signal (orange), and (iii) moving average output (blue).

Figure 2

 2 Figure 2.5 -Device attitude. (a) The device frame (D) and the Earth frame (E). (b) The orientation of the device frame (D) relative to Earth frame (E) in terms of Euler angles.

  . The first one requests feature engineering (shallow learning), where the extraction of handcrafted feature vectors from raw data signals is done manually.Those vectors are the input of a classifier, leading to the classification of the corresponding physical activity. In the literature, time-domain and frequency-domain features were proposed such as mean, median absolute deviation, interquartile range, entropy[START_REF] Bao | Activity recognition from user-annotated acceleration data[END_REF][START_REF] Reyes-Ortiz | Transition-aware human activity recognition using smartphones[END_REF][START_REF] Yang | Using acceleration measurements for activity recognition: an effective learning algorithm for constructing neural classifiers[END_REF], as well as the Fast Fourier Transform (FFT) coefficients and spectral power[START_REF] Bonomi | Detection of type, duration, and intensity of physical activity using an accelerometer[END_REF][START_REF] Xie | Human activity recognition method based on inertial sensor and barometer[END_REF] to name a few. The computational complexity of such techniques, expressed in floating-point operations per second (flops), varies depending on the number of extracted features and their implementation. For instance, the logarithm/exponential operation is much more complex than the other basic operations like addition and multiplication, since a software library is usually developed for its computation instead of a hardware implementation. After being experimentally tested in parallel on a microcontroller with a Floating-Point Unit (FPU) single precision, the multiplication and division operations displayed almost the same complexity, whereas the logarithm/exponential was 25 times more complex. This notion is important for embedded solutions considering the limited power resources of a micro-controller, since the prediction operation demands very low latency in real-time applications. Otherwise, researchers may resort to remote servers for high complexity algorithms. The feature vectors constitute the input of a classifier to recognize the gesture over a certain window. In the context of embedded algorithms in wearable sensors, some low-cost classifiers, like Decision Tree (DT) and Support Vector Machine (SVM) with linear/quadratic kernel, may be preferred to memory-based ones such as k-Nearest Neighbors (KNN), which raise the computational complexity of the system (see Appendix C for details).On the other hand, deep learning techniques have been also implemented to develop HAR systems, where feature extraction is done automatically from raw signals to learn and make intelligent decisions. Unlike shallow learning techniques, the benefit of deep learning approaches is their ability to learn automatically from raw data. They do not require strong expertise in feature engineering. For instance, Convolutional Neural Network (CNN)[START_REF] Ha | Convolutional neural networks for human activity recognition using multiple accelerometer and gyroscope sensors[END_REF][START_REF] Zeng | Convolutional neural networks for human activity recognition using mobile sensors[END_REF] and Recurrent Neural Network (RNN)[START_REF] Li | Smartphone-sensors based activity recognition using indrnn[END_REF] were proposed. The Long-Short Term Memory (LSTM) network, which is a type of recurrent networks, was also developed for this purpose (Y.[START_REF] Chen | Lstm networks for mobile human activity recognition[END_REF]. LSTM addresses the vanishing/exploding gradient problem that can happen with RNN. However, its reliability is affected by the size of the training set. Therefore, a third architecture of recurrent networks has been proposed, namely Gated Recurrent Unit (GRU) network, which (i) is faster than LSTM, and (ii) can outperform it (S.[START_REF] Yang | Lstm and gru neural network performance comparison study: taking yelp review dataset as an example[END_REF]. More recently, Chen et al. proposed a Feature Fusion (FeFu) technique (Z.[START_REF] Chen | Smartphone sensor-based human activity recognition using feature fusion and maximum full a posteriori[END_REF]. It consists of two separate modules: (a) handcrafted features followed by fully connected layers, and (b) automatic feature learning (deep learning). The outputs of both modules are concatenated to predict the activity. Considering the large computational load of such techniques and the amount of resources required to run them, their embeddability is out of question. Therefore, data acquisition (via wearable sensors) and decision making (remote server)

  Five positions were covered, namely right pocket, waist, chest, wrist, and ankle. Nonetheless, F s was set to 20 Hz, which might be insufficient for capturing certain ADLs. HAPT (Human Activities and Postural Transitions) is another set of data collected using a waist-worn smartphone(Anguita et al., 2013). Signals of 12 ADLs/postures were recorded at 50 Hz using an accelerometer and a gyroscope. Although F s is relatively larger than that of the previous dataset, it only covers one position and does not consider any magnetometer, thus MARG-based solutions cannot be tested on this dataset. Likewise, SisFall consists of 19 ADLs and 15 falls(Sucerquia et al., 2017).

  both shallow learning and deep learning applications. These files are stored in comma-separated values (csv) format. A MATLAB script was created to convert the dataset into a MATLAB structure stored as a ".mat" file. Another Python script was created to convert the dataset into a Pandas dataframe stored in hdf (".h5") or pickle (".pkl") formats. The corresponding files and scripts are available on IEEE DataPort: http://dx.doi.org/10.21227/bnya-mn34 and Appendix D summarizes the characteristics of this dataset. FallAllD could be used for fall detection, by considering a binary classification (Fall vs Activity), and for HAR (multinomial classification) by keeping the targeted activities (acquired signals related to the targeted ADLs) and excluding the rest (the remaining data). FallAllD is used to train our machine learning models and evaluate their performance as previously explained.2.4.1.1 Devices and CharacteristicsRF-Track, our industrial partner, developed three identical data-loggers to collect motion signals. These data-loggers can be worn around the neck, the wrist, and the waist. A data-logger was equipped with the inertial module LSM9DS1, featuring (i) a tri-axial digital MEMS accelerometer, with A F s = 238 Hz and m R = ±8 g, (ii) a tri-axial gyroscope with G F s = 238 Hz and an angular rate of ±2000 dps, (iii) a tri-axial magnetometer with M F s = 80 Hz and a full scale magnetic field of ±4 Gauss. Although the aforementioned sampling frequencies are high and inappropriate for embedded solutions, this choice was made for research purposes. With

  Reason of fall: syncope, trip, slip, losing balance • Direction of fall: forward, backward, lateral, straight (ending sitting) • Final posture: sitting, lying A wide-range of ADLs and human gestures were also considered in this dataset. The simulated activities can be divided into four main categories: • Cyclic ADLs: (a) walking (slowly and quickly), (b) jogging (slowly and quickly), (c) climbing stairs up and down (slowly and quickly). • Transient phases of cyclic ADLs: (a) walking (start and stop), (b) jogging (start and stop), (c) climbing stairs up and down (start and stop). • Transient ADLs: (a) sitting down (stand-to-sit, walk-to-sit), (b) standing up (sit-to-stand, sit-to-walk), (c) failing to stand up, (d) lying down on a bed, (e) rising up from a bed, (f) changing position while lying, (g) stumbling while walking (without falling), (h) jumping (slightly and strongly), (i) bending down. • Hand gestures: (a) clapping hands (one time and continuously), (b) waving hands, (c) shaking hands, (d) raising hand up, (e) moving hand down, (f) moving hand up then down

Figure 2 .Figure 2 . 6 -

 226 Figure 2.6 -The printed circuit board with the corresponding components.

  in detail the developed techniques to recognize and predict the performed activities based on segmented signals. It begins by listing the targeted ADLs with their corresponding acceleration patterns and characteristics. Afterwards, three different techniques are proposed.We first consider a wrist-worn device (which was subject to a parallel study on fall detection) in order to monitor the physical activity. The proposed technique is low-cost and particularly adapted for cyclic activities. However, the arm is likely to move randomly when performing any activity, which may lead to an erroneous classification in real situations.Moreover, the body posture is not precisely estimated by a sensor worn around the wrist. Therefore, we consider two other approaches, which are complete HAR mechanisms and concern the body trunk (waist-worn and necklace/chest-worn devices). Hence, recurrent movements, postural transitions, and inactivity periods are considered by these methods. One of them is a high complexity technique, based on an AHRS, and involves deep learning networks. It cannot be executed on a micro-controller in real-time, thus remote servers are needed to process acquired data and predict the ADLs. The second one is a low complexity technique, based exclusively on acceleration signals to meet industrial constraints (mainly related to power consumption) and to be embedded in the device since it requires very low latency (few flops). Both techniques ensure a step-by-step recognition by providing a decision every second. The aforementioned approaches are compared to state-of-the-art methods, by extracting a set of classical widely used features

Figure 3

 3

Figure 3 . 1 -

 31 Figure 3.1 -Acceleration signals {a X , a Y , a Z } captured from the human body trunk and representing the targeted ADLs.

Figure 3 . 2 -

 32 Figure 3.2 -Magnitude ||a|| of acceleration signals resulting from "Jogging" and "Walking" respectively.

Figure 3 .

 3 Figure 3.3 illustrates the organizational chart representing the aforementioned remarks. The approach begins by preprocessing the signal in order to determine the category of the activity. So, wrist movements are firstly divided into the three main categories, namely cyclic, transient, and inactivity. Inactivity periods are considered by this solution, whereas transient activities are filtered out. Additionally, when a cyclic activity is detected, the solution discriminates between four different classes based on a machine learning algorithm. These four classes are: cyclic activities resulting from constant shocks (C-1), and hand waving (C-2), cyclic activities resulting from

Figure 3 . 3 -

 33 Figure 3.3 -Organizational chart justifying the choice of the considered classes for wrist-worn tracker.

(

  250 ms) overlapping. For each segment, we calculate the local maximum M k , the local minimum m k and the local range r k = M k -m k . If three or more consecutive local ranges are below 0.5 g, or if two or more non-consecutive segments represent a local range below 0.5 g, the window is labeled as 'Transient'. This means that the subject was inactive for at least 1 s and moved during the remaining 2 s, or was barely moving during these 3 s. As indicated previously, we neglect such activities in the present study (the algorithm stops when a transient activity is detected).

Figure 3 . 4 -

 34 Figure 3.4 -Proposed peak detection technique: a λ (j) satisfying Eq. (3.1) (red crosses) and the actual peaks (black circles).

Figure 3 .Figure 3

 33 Figure 3.5.b), and abs_Dx another array consisting of their absolute values. Suppose that M is the number of points in abs_Dx that exceed 0.2 g and N the number of times where two

Figure 3 .

 3 Figure 3.6.a illustrates the distribution of data-points following the first two features (prominence and width) in the 2D space. Clusters representing the four classes appear clearly in this space

Figure 3 . 6 -Figure 3

 363 Figure 3.6 -Data distribution. (a) The 2D distribution of activities following the first two features (Prominence vs Width). (b) The SVM L hyperplane in 3D space (C-2 vs C-3) after adding a third feature (Entropy) and its intersection with the (Entropy, Width) 2D plane. (c) The SVM Q hyperplane in 3D space (C-1 vs C-4) after adding a third feature (Variability).

(

  as shown in Figure 3.11): U stands for 'up', D stands for 'down', F stands for 'front', B stands for 'back', L stands for 'left', R stands for 'right'. Acquired raw data are integers. As indicated previously, the acceleration values are multiplied by a constant C A to convert them into g units, the angular velocity values by C G to convert them into • /s, and the magnetic field values by C M to transform them into Gauss. These constants are equal to 2ρ/2 γ , where ρ is the sensor measurement range and γ is the sensor resolution. The corresponding instructions and commands are detailed below. The algorithm begins by reading data, converting them, and storing them in arrays. Quaternions Q are updated using Madgwick's orientation filter, and Euler angles are then calculated, when an acceleration value

Figure 3 . 9 -Figure 3 .Algorithm 2 4 :

 39324 Figure 3.9 -Acquisition cycle when (i) all modalities have the same sampling rate (configuration λ 1 ) and (ii) the magnetometer has a lower rate (configuration λ 2 ), particularly A F s = G F s = 60 Hz and M F s = 40 Hz.

Figure 3 .

 3 Figure 3.11 illustrates the orientation of the wearable device during a forward fall while walking caused by a syncope (fainting). Two moments are identified: the first one (left graph)

Figure 3 .

 3 Figure 3.11 -Wearable sensor orientation when the subject is walking (left graph), when the human body is hitting the ground during the impact phase of the fall (right graph).

Figure 3 .

 3 Figure 3.12 -The proposed HAR mechanism, consisting of two deep learning networks (CNN & LSTM) and a fully connected network (dense layers).

  60 Hz and M F s = 40 Hz. Acceleration and angular velocity signals were downsampled by a factor of 4 (238 Hz → 60 Hz) and magnetic field signals were downsampled by a factor of 2 (80 Hz → 40 Hz). This choice was made since the targeted orientation filter achieves similar levels of performance above a 40-50 Hz sampling rate (Madgwick, 2010). For transient ADLs, i.e. C 1 , C 2 , C 3 , and C 4 , the signals were segmented using seven 6-second windows: the one centered on the transition moment, and six others shifted by ±125/±250/±500 ms. Afterwards, five out of seven windows were chosen randomly. The same goes for the remaining activities (C 9 ), where falls from three different initial body postures were considered, namely (i)

  Figure 3.13 -Confusion matrix (showing the rates in %) of (a) the 9-class model and (b) the 8-class model after combining C 5 and C 6 into one class C 5 .

Firstly

  , the subject is either active or inactive (C 7 ). If he is active, the corresponding movements are the result of (i) a change in the trunk orientation, i.e. (C 3 ) lying down or (C 4 ) rising up, (ii) a sudden change of movements intensity evolving a rapid change in acceleration level, i.e. activities to be excluded (C 8 ) like jumping and falling, or (iii) a remaining activity. The remaining ADLs can finally be separated into cyclic (i.e. recurrent movements) and transient movements. ADLs reaching the cyclic node are either (C 5 ) walking or (C 6 ) jogging. The weightlessness state (Z. He Movement Sitting down (𝐶 2 ) Standing up (𝐶 8 ) Non-postural (𝐶 8 ) Intensity

Figure 3 .

 3 Figure 3.14 -Organizational chart showing the possible movements of an elderly from a trunkplaced device point of view. The blue leaves represent the targeted ADLs and the red leaves represent the activities to be excluded.

  us detail the aforementioned operations. Mean values: we consider a sliding window of length L and a sampling frequency equal to F s .

  For x-component and z-component, m = L and n = F s , whereas for ||a||, m = 2L and n = Fs 2 . Consequently, at each decision, the mean value of the i-th segment is computed based on λ i and c = 1 n (Eq. (3.6)):

Figure 3 .

 3 Figure 3.16 -Online computation technique consisting of m buffers ζ [i] of length n. The red arrows indicate the propagation of acquired data-points. For each new read value ν, the ζ [i] j

Figure 3 .Figure 3 .

 33 Figure 3.19 -Heatmap consisting of the achieved accuracy (%) for each (F s , L) pair after applying MDA.

Figure 3 .

 3 Figure 3.20 -Performance of MDA in terms of precision and recall for each targeted activity using 1-vs-all strategy.

  and 3.18), d = 5 (F L+1,...,2L ) and k = 3 (Transient, Inactivity, Cyclic) when it comes to stage S1, d = 10 (F 1,...,2L ) and k = 3 (Orientation, None, Intensity) for S2, d = 15 (F L+1,...,4L ) and k = 2 (Walking, Jogging) for S3 (II-c), and d = 15 (F 2L+1,...,5L ) with k = 3 (Sitting down, Standing up, Others) for S3 (III-c). So, the complexity of each stage (leaf) is indicated hereafter: {'S1': 123 flops, 'S2': 183 flops, 'S3 (II-c)': 232 flops, 'S3 (III-c)': 243 flops} -→ 123 flops (inactivity) ≤ Ξ ≤ 549 flops (transitions)

Figure 3 .

 3 Figure 3.22 -Output of HAR module. (a) The step by step recognition using a sliding window with overlapping. (b) The raw output of HAR technique (list of decisions) and its transformation into an array summarizing the succession of performed ADLs with the indices of the sliding windows, the corresponding duration (in seconds), and status (active/inactive).

  possess low SD values (less than 3% for example) and low range values (below 0.1 g). Afterwards, windows consisting of consecutive silent fragments are detected, and the corresponding duration S is measured. Sleeping cycles are windows where S exceeds 5 minutes. The sleeping time (SpT) is equal to the sum of cycles' lengths. Bed time (BdT) is the time spent between the first and

Figure 4 .Figure 4 . 2

 442 Figure 4.1 -Human behavior vs acceleration magnitude ||a|| while walking (recurrent movements).

Figure 4 . 2 -

 42 Figure 4.2 -Magnitude ||a|| of two signals with the same SD value.

Figure 4 .

 4 Figure 4.5 displays the box plots for the eight extracted features (after being scaled). For each box plot, the line inside each box is the median of the samples, while the top and bottom edges are the Q 3 and Q 1 , respectively. The distance between both edges is the Interquartile Range (IQR). Outliers are values exceeding 1.5×IQR away from the top or bottom of the box, and

Figure 4 . 5 -

 45 Figure 4.5 -Box charts showing the data distribution of each feature (x-axis) for both populations (Robust vs Frail).

Figure 4 .

 4 Figure 4.6 -Performance of NN (using the voting technique) as a function of time (in days) in terms of Sensitivity (Sen), Specificity (Spe), and Accuracy (Acc).

Figure 4 .

 4 7.a illustrates the magnitudes of three acceleration signals, each one associated to a subject belonging to one of the three populations: (i) Robust, (ii) Pre-frail, and (iii) Frail. The orange parts correspond to the same signals after truncating the 25% lowest and highest data-points. The proposed six gait parameters are introduced hereafter: Feature F 1 : the range of orange signals in Figure 4.7.a decreases when the subject becomes frail. It means that the intensity of the movements and the generated power while walking decrease. Feature F 1 is the 25% trimmed range of the acceleration magnitude ||a||. It is the range of the signal after excluding the highest and lowest k values, with k = N 2 × 25 100 and N being the length of the signal. Suppose that ||a|| is the truncated acceleration magnitude (orange signal in Figure 4.7.a), hence:

Figure 4 .Feature F 2 :

 42 Figure 4.7 -Gait signals. (a) Acceleration magnitude ||a|| representing the gait of each population (steps in red circles) and (b) the auto-correlation values as a function of a lag τ .

Figure 4 .

 4 7.billustrates the auto-correlation signal (τ = 1, ..., T , with T = 20) for each population. It is clear that A(τ ) is regular for the robust (healthy) subject. However, the sinusoidal shape vanishes while heading towards the frail status, since the periodicity disappears in the acceleration signals, meaning that the gait loses its fluidity. The information carried by A(τ ) is encoded in a third feature F 3 , by calculating the distribution entropy of this autocorrelation signal. The entropy quantifies the unpredictability or the randomness of A(τ ), which is partitioned into 10 equal intervals of size W . If the number of points in the i th interval is equal to t i :

Figure 4 .

 4 10. The corresponding accuracy increases by increasing n, and is somewhat saturated beyond 45 estimators. Hence, with more than 20 estimators, RF becomes one of the top performers. Nonetheless, increasing n indefinitely induces overfitting and thus prevents the generalization of the model (the ability of a trained model to classify unseen

Figure 4 .

 4 Figure 4.9 -Data distribution of the three populations following three principal components pc 1 , ..., pc 3 .

Figure 4 .

 4 Figure 4.11 illustrates the confusion matrix, based on the output of SVM R (the best classifier according to Table 4.8). The columns represent the target class or the ground truth, while the rows represent the predicted class or the output of the classifier. The diagonal elements constitute the correct decisions. For instance, 92.3% of gait signals belonging to robust elderly are well classified. However, 5% of those signals are misclassified as pre-frail and the remaining 2.7% as frail. The highest confusion occurs with the pre-frail class for which 11.3% of signals linked to this population are classified as robust, and 2.1% of those signals are categorized as

Figure 4 .

 4 Figure 4.10 -Accuracy (%) of RF as a function of the number of estimators n.

Figure 4 .Figure 4 .

 44 Figure 4.13 -History of two activity metrics (steps and activity rate) on a daily basis over the past week.

Figure 4 .

 4 Figure 4.14 -History of gait periods in a specific day with the corresponding time and duration.The corresponding gait parameters and the predicted frailty status appear on the screen when the user selects a cell.

  ditions. In other words, a Natural Language Processing (NLP) module can be developed to analyze the speech of elderly and their responses to certain questions. The frailty cycle (Figure1.2) includes cognitive impairment, depression and dementia. It is worth mentioning that cognitive, behavioral, social and psychological status could be quite useful to extract indicators for frailty. All these aforementioned factors are acquired by asking questions and collecting answers as texts. In this context, the role of NLP is huge: it is essential to analyze these texts and to extract some patterns and useful indicators of frailty. As a matter of fact, the exhaustion for example, which is one of FrP criteria, cannot be estimated by an accelerometer. Nonetheless, with NLP, this issue could be resolved. The same remark holds for other parameters such as pain perception and anxiety. Note that verbatim transcription is needed since the order of the words in a sentence and the expressed words/vocabulary are of great importance. The Bidirectional Encoder Representations from Transformers (BERT), which is a transformer-based machine learning technique for NLP (developed by Google), might be considered in this context.

1.

  During the past month, at what time have you usually gone to bed at night? 2. During the past month, how long (in minutes) has it usually taken for you to fall asleep at night? 3. During the past month, at what time have you usually gotten up in the morning? 4. During the past month, how many hours of actual sleep did you get at night? 5. During the past month, how often have you had trouble sleeping because you: (a) Cannot get to sleep within 30 minutes (b) Wake up in the middle of the night or early morning (c) Have to get up to use the bathroom (

  can solve the Gimbal lock issue. Applying quaternions can be seen as a direct transformation from a certain orientation to another one, rather than breaking this transformation into a series of rotations. Now, by setting the equilibrium as the reference point, i.e. -ks + m 0 g = 0, Eq. (E.1

  Abbas, M., & Le Bouquin Jeannès, R.(2020). Characterizing peaks in acceleration signals-application to physical activity detection using wearable sensors.IEEE Sensors Journal, 20 (20). Abbas, M., & Le Bouquin Jeannès, R. (2021). Exploiting local temporal characteristics via multinomial decomposition algorithm for real-time activity recognition. IEEE Transactions on Instrumentation and Measurement, 70, 1-11. Abbas, M., Somme, D., & Le Bouquin Jeannès, R. (2021). D-sorm: a digital solution for remote monitoring based on the attitude of wearable devices. Computer Methods and Programs in Biomedicine, 208, 106247. Abbas, M., Somme, D., & Le Bouquin Jeannès, R. (2020). Machine learning-based physical activity tracking with a view to frailty analysis. 42nd Annual International Conference of the IEEE Engineering in Medicine Biology Society (EMBC), 3917-3920. Abdelhafiz, A., & Sinclair, A. (2015). Low hba1c and increased mortality risk-is frailty a confounding factor? Aging Dis, 6 (4), 262-270. Afzal, M., Renaudin, V., & Lachapelle, G. Assessment of indoor magnetic field anomalies using multiple magnetometers. In: In proceedings of 23rd international technical meeting of the satellite division of the institute of navigation. 2010, 525-533. Albarbar, A., & Teay, S. H. (2017). Mems accelerometers: testing and practical approach for smart sensing and machinery diagnostics. In D. Zhang & B. Wei (Eds.), Advanced mechatronics and mems devices ii (pp. 19-40). Springer International Publishing.Alvarez-Ríís, A., Guerrero, J., García-García, F., Rodríguez-Mañas, L., Medrano-Campillo, P., de la Torre Lanza, M.,Alvarez-Sánchez, N., & Carrillo-Vico, A. (2015). Associations between frailty and serum n-terminal propeptide of type i procollagen and 25hydroxyvitamin d in older spanish women: the toledo study for healthy aging. ExpGerontol, 69, 79-84. Anguita, D., Ghio, A., Oneto, L., Parra, X., & Reyes-Ortiz, J. L. (2013). A public domain dataset for human activity recognition using smartphones. European Symposium on ArtificialNeural Networks (ESANN).Apsega, A., Petrauskas, L., Alekna, V., Daunoraviciene, K., Sevcenko, V.,Mastaviciute, A., Vitkus, D., Tamulaitiene, M., & Griskevicius, J. (2020). Wearable sensors technology as a tool for discriminating frailty levels during instrumented gait analysis. Applied Sciences, 10 (23).

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  doi: 10.1109/EMBC44109.2020.9175589. • M. Abbas, M. Saleh and R. Le Bouquin Jeannès, "A Hybrid Solution for Human Activity Recognition: Application to Wrist-Worn Accelerometry," 2019 Fifth International Conference on Advances in Biomedical Engineering (ICABME), 2019, pp. 1-4. → doi: 10.1109/ICABME47164.2019.8940233. • M. Saleh, N. Georgi, M. Abbas and R. Le Bouquin Jeannès, "A Highly Reliable Wrist-Worn Acceleration-Based Fall Detector," 2019 27th European Signal Processing Conference (EUSIPCO), 2019, pp. 1-5. → doi: 10.23919/EUSIPCO.2019.8902563. National Conferences • M. Abbas, J. Prud'homm, F. Lemoine, D. Somme, and R. Le Bouquin Jeannès, "Device Attitude and Real-Time 3D Visualization: An Interface for Elderly Care," Colloque en TéléSANté et dispositifs biomédicaux (Jetsan), Mai 2021. → link: Abbas et al. -JetSan 2021. • J. Prud?homm, F. Lemoine, M. Abbas, G. Carrault, D. Somme, and R. Le Bouquin Jeannès, "A priori acceptability of a multimodal system for the early detection of frailty in older adults," Colloque en TéléSANté et dispositifs biomédicaux (Jetsan), Mai 2021. → link: Prud'Homm et al. -JetSan 2021.

Titre:

  Détection et analyse de l'activité physique chez les personnes âgées à l'aide de capteurs portables pour l'évaluation de la trajectoire de fragilisation Mots-clés : détection, classification, signaux physiologiques, capteurs, activité phyique, telemonitoring

Abstract:

  Frailty is a geriatric syndrome characterized by physiological weakening that would affect 4 out of 5 people over 85 years old in France. In this context, our work consisted in proposing a wearable sensor-based fully automated system to monitor the activity of elderly with a view to analyze the frailty trajectory. This system consists of two layers, namely a machine learning-based human activity recognition (HAR) module to detect activities of daily living (ADLs), and a second module to analyze the ADLs. Regarding the first module, two HAR approaches were developed. The first one considers data acquired from an accelerometer, a gyroscope and a magnetometer, and is highly complex, based on sensing unit orientation, com-bining both handcrafted features and deep learning networks. The second one is an embeddable solution which exploits local temporal characteristics of acceleration signals exclusively. Once localized, the ADLs represented by windowed timeseries feed the second module. Here, two types of activity and health metrics are extracted from windowed data to assess the health conditions of elderly, namely global features which are computed over the course of a day, and local features which characterize the gait. A longitudinal study on data acquired under unsupervised conditions during the daily life of senior citizens (robust, pre-frail and frail) attested to the effectiveness and feasibility of our solution.

Table 1 -

 1 Les accéléromètres MEMS vs PEC suivant différents attributs

	Attribut	MEMS (I) PEC (II)	Commentaire
	Faible coût		(II) difficile à produire en masse
	Faible consommation d'énergie		(II) a besoin d'une amplification
	Haute température		Jusqu'à 350 • C
	Gamme haute fréquence		> 500 Hz
	Choc à fort impact		> 200 g
	Insensible à l'humidité
	Accélération statique (gravité)

  Les quatre classes ont été simulées suivant un protocole expérimental prédéfini. Cependant, le bras peut bouger de manière aléatoire lorsqu'on effectue une certaine activité, ce qui affecte le modèle du signal et conduit donc à une classification erronée. La précision obtenue ne reflète pas nécessairement les performances du système dans des situations réelles. De plus, les transitions posturales ne sont pas captées à partir de cet emplacement. La posture du corps, qui peut être un point sensible dans notre contexte, n'est pas précisément estimée par un capteur porté au poignet. Par conséquent, ce dispositif est insuffisant pour le dépistage de la fragilité, et les ADLs ne doivent pas être analysées à partir de cette position.

). Il convient de mentionner qu'en moyenne, la SVM a été sollicitée dans 41,87% des cas. En d'autres termes, environ 60% des données des ensembles de test ne tombent pas dans les ZIs, et la prédiction est donc effectuée par le modèle DT (utilisant seulement deux caractéristiques).

b) Dispositif placé sur le tronc

Les résultats expérimentaux montrent l'efficacité de l'approche proposée pour les trackers portés au poignet dans des conditions supervisées. Néanmoins, plusieurs limitations et inconvénients sont notés.

i) Approche basée sur l'orientation du dispositif

Nous proposons maintenant une méthode de reconnaissance qui (a) assure une visualisation du dispositif portable (unité de détection) en temps réel et (b) prend une décision à chaque seconde en prédisant l'activité réalisée. Elle est basée sur le capteur MARG. L'objectif est donc d'estimer l'orientation du dispositif portable pour prédire le mouvement effectué. Les angles d'Euler (ψ, θ, φ) décrivent cette orientation dans le repère terrestre E, obtenue par des rotations séquentielles de ψ autour de z E , θ autour de y E , et φ autour de x E

[START_REF] Kuipers | Quaternions and rotation sequences: a primer with applications to orbits, aerospace and virtual reality[END_REF][START_REF] Madgwick | An efficient orientation filter for inertial and inertial / magnetic sensor arrays[END_REF]

. Par conséquent, pour afficher le dispositif portable en temps réel, une plateforme a été développée. (x, z) est le plan de l'écran, et y est l'axe perpendiculaire au plan précité. Le boîtier est symbolisé par un parallélépipède centré à l'origine. L'algorithme commence par lire les données, les convertir et les stocker dans des tableaux. Les angles d'Euler sont calculés à l'aide de l'algorithme de Madgwick

[START_REF] Madgwick | Estimation of imu and marg orientation using a gradient descent algorithm[END_REF]

. Après ξ acquisitions, le graphe 3D est mis à jour en faisant tourner les points médians entre les sommets opposés autour des axes. La Figure 6 illustre l'orientation du dispositif portable lors d'une chute vers l'avant en marchant, chute causée par une syncope (évanouissement). L'attitude du dispositif (angles d'Euler estimés) sur une période donnée fournit des indices importants pour reconnaître les activités physiques. Les mouvements successifs du tronc doivent maintenant être exploités pour détecter les ADLs. Les classes ciblées par cette approche sont (C 1 ) s'asseoir, (C 2 ) se mettre debout, (C 3 ) s'allonger, (C 4 ) se lever, (C 5 ) marcher, (C 6 ) monter/descendre des escaliers, (C 7 ) faire du jogging et (C 8 ) inactif. De plus, et puisque les êtres humains peuvent effectuer un large éventail d'activités ou de mouvements dans leur routine quotidienne, qui ne sont pas pris en compte par le modèle de reconnaissance, une neuvième classe (C 9 ) appelée "autre" est considérée pour filtrer/exclure les activités qui ne sont pas ciblées par notre système (comme sauter et chuter par exemple). Une fenêtre d'analyse de 6 secondes est choisie pour cette tâche, i.e. une prédiction est faite après traitement des mouvements sur une durée de 6 s. Le processus de reconnaissance que nous proposons est basé sur la fusion de caractéristiques (à la fois des caractéristiques extraites manuellement et d'autres extraites automatiquement). Les angles d'Euler alimentent un réseau de neurones récurrent, à savoir Long-Short z-axis z-axis Figure 6 -Orientation du capteur portable lorsque le sujet marche (graphique de gauche), lorsque le corps humain heurte le sol pendant la phase d'impact de la chute (graphique de droite). Term Memory (LSTM). Ce réseau est défini par une seule couche de 100 unités de mémoire. Un autre module d'apprentissage profond est ajouté, à savoir un réseau de neurones convolutif CNN (Convolutional Neural Network). Ce réseau est alimenté par des signaux d'accélération, afin de capter leurs formes/silhouettes. Ce réseau est défini par cinq couches convolutionnelles, composées respectivement de 16, 32, 64, 128 et 256 filtres. La taille du filtre de la première couche est de 9×3, tandis que la taille du filtre des autres couches est de 9×1. Ces couches sont suivies d'une couche de « Max Pooling », afin de réduire le phénomène de surapprentissage. Enfin, un troisième réseau de neurones composé de trois couches entièrement connectées (Dense) est également ajouté. Le nombre de neurones de chaque couche est respectivement 40, 20 et 10. Ce réseau est alimenté par 18 caractéristiques extraites manuellement à partir des signaux d'accélération et des angles d'Euler. Tout d'abord, l'amplitude de l'accélération ||a|| est calculée comme a 2 x + a 2 y + a 2 z . Deuxièmement, ||a| et les angles d'Euler sont divisés en trois segments égaux de 2 s, et les valeurs moyennes de ces segments sont calculées, résultant en 12 caractéristiques. Troisièmement, la corrélation entre chaque paire d'angles d'Euler {ψ, θ, φ} est calculée.

Table 2

 2

illustre la précision correspondante pour chaque méthode, montrant la supériorité de la technique proposée qui atteint une précision de 97,7%. Comme prévu, fusionner la sortie de plusieurs types de réseaux de neurones augmente le pouvoir de discrimination du processus de classification. Une grande confusion est repérée entre les classes (C 5 ) marcher et (C 6 ) monter/descendre des escaliers.

Pour éviter ce problème, on peut fusionner les classes (C 5 ) et (C 6 ) en une seule classe (C 5 ).

Dans ce cas, la précision atteint 98,68%. Par suite, on peut ajouter un baromètre (qui estime l'altitude) pour discriminer entre marcher, monter et descendre les escaliers quand la sortie de l'algorithme est (C 5 ). Plus de détails sur cette méthode et les résultats expérimentaux se trouvent dans

[START_REF] Saleh | Fallalld: an open dataset of human falls and activities of daily living for classical and deep learning applications[END_REF]

. Un prototype a été créé et sa fonctionnalité est présentée dans une vidéo (Supplementary Data S2) via ce lien : https://www.sciencedirect.com/science/ article/pii/S0169260721003217.

ii) Approche basée sur l'accélération

Il est clair que la complexité de la méthode précédente est très élevée. Cette approche doit être exécutée sur un serveur distant disposant de ressources énergétiques élevées pour fonctionner

Table 2 -

 2 Résultats expérimentaux comparant les techniques de détection d'activités en termes de précision (%)

	Classifieur	CNN LSTM	MP	KNN	DNN	RF	RS
	Entrée	SigBr † SigBr SigBr + Carac Carac* Carac Carac Carac
	Précision (%) 93.81	76.71	97.7	90.85	86.12 89.31 76.13
	† Signaux bruts -* Caractéristiques

Table 3 -

 3 Précision obtenue lorsque le modèle est entraîné sur FallAllD et testé sur les autres bases de données Plus de détails sur cette méthode et les résultats expérimentaux se trouvent dans (Abbas et Le Bouquin Jeannès, 2021). Un prototype a été créé et sa fonctionnalité est présentée dans une vidéo (Abbas et Le Bouquin Jeannès, 2021) via ce lien : https:

	Base de données SisFall mHealth HAPT UMAFall
	Précision	97.75% 96.95% 94.12%	92%
	(nouveaux sujets, accéléromètres et protocoles expérimentaux différents). La Table 3 illustre les
	résultats correspondants. MDA évite le surapprentissage puisqu'il encode les caractéristiques
	temporelles locales.

//ieeexplore.ieee.org/document/9528906/media#media.

4 Analyse de la fragilité

La section précédente a présenté le premier module du système de télésurveillance, qui est lié à la détection des activités. Maintenant, une fois ces activités détectées et localisées, un deuxième module doit les analyser afin d'évaluer les conditions de fragilité des personnes âgées et de détecter la détérioration de leur fonction physique. Ce deuxième module est détaillé dans cette section, en décrivant deux types de métriques d'activité, qui sont associés à l'état de fragilité.

a) Caractéristiques globales d'activité

Un ensemble de caractéristiques hétérogènes est extrait pour caractériser la fonction physique.

Ces variables, appelées variables globales, sont calculées au cours d'une journée. Cinq caractéristiques pertinentes sont extraites des données fenêtrées afin de prédire le statut de fragilité du sujet. La Variable V 1 est le nombre de pas. Cette caractéristique est représentée par le nombre de pics dans les signaux d'accélération lorsque le sujet marche/fait du jogging (selon la sortie du module précédent, i.e. détection des activités). La Variable V 2 révèle le nombre de fois où le sujet a monté/descendu des escaliers par jour. Lorsque la sortie du module précédent est "Marcher", les signaux barométriques sont inspectés pour voir si l'altitude augmente/diminue. Dans notre solution, une différence de 3 mètres est équivalente à un étage. La Variable V 3 est une approximation de la dépense énergétique. Cette variable quantifie le nombre de calories brûlées à l'aide de l'équation suivante :

Calories (kcal) = MET × Durée (h) × Poids (kg)

Le type d'activité physique, son intensité (écart-type de ||a||), et l'intervalle de temps correspondant (durée) sont connus grâce au module précédent. En fonction du type et de l'intensité des

Table 4 -

 4 Les équivalents MET en fonction du type de l'activité et de son intensité

	État	Type et Intensité MET
	Inactif	-		1
		Mouvements légers	1.5 -2
			Faible	2
	Actif	Périodique	Modéré	3.3
			Vif	5
		Jogging	> 6
	mouvements, une valeur MET est attribuée à l'aide de la

Table 4 (

 4 [START_REF] Haskell | Physical activity and public health: updated recommendation for adults from the american college of sports medicine and the american heart association[END_REF]. Les deux dernières caractéristiques sont liées aux périodes de périodicité par jour. Ces variables me-

	correspondants. NN atteint la plus grande précision et la plus grande sensibilité (92,88%), ce
	qui représente la capacité d'un classifieur à identifier correctement les personnes fragiles dont la
	fonction physique est endommagée. GBM a le plus faible taux de faux positifs (4,73%). Ainsi,
	si l'on veut avertir le personnel médical que le sujet devient fragile (sur une base quotidienne),

surent la durée de la marche/du jogging continu (sans arrêt) et leur période correspondante (en secondes). En conséquence, la séquence d'autocorrélation des fenêtres d'analyse de 30 secondes (où la personne âgée marche/fait du jogging) est calculée. Ensuite, les pics de la séquence résultante, dont les valeurs dépassent 0,3, sont détectés et localisés. La sortie de l'autocorrélation doit présenter au moins 3 pics afin de considérer le mouvement comme périodique. La Variable V 4 est égale à la somme des cycles de périodicité (le temps pendant lequel le sujet effectue une activité périodique) et la Variable V 5 est égale à la valeur moyenne des différences entre les positions des pics consécutifs, qui est équivalente à la période du cycle de la marche (stride). Les données de la base de données ActFreeLi ont été utilisées pour évaluer la capacité de ces variables à détecter un affaiblissement physique. La population étudiée était parfaitement équilibrée (50% fragiles et 50% robustes). En moyenne, les participants ont été suivis pendant 31,6 (± 16,5) jours, ce qui donne un total de 570 jours d'enregistrements. Ces sujets, dont le poids était compris entre 54 et 85 kg et la taille entre 150 et 171 cm, ont porté le dispositif au cours de leur vie quotidienne sans aucune instruction spécifique. Les cinq caractéristiques globales susmentionnées ont été extraites des données brutes, représentant ces cinq mesures d'activité à l'échelle quotidienne. Elles ont été soumises à cinq classifieurs d'apprentissage automatique, à savoir un réseau de neurones NN d'une couche cachée de 15 neurones avec une fonction d'activation sigmoïde, une machine à vecteur de support SVM dont le noyau est à base radiale, la méthode des k plus proches voisins KNN avec k = 5, la forêt d'arbres décisionnels RF de 10 estimateurs et une profondeur maximale égale à 5, et le boosting de gradient GBM (Gradient Boosting Machine) de 100 estimateurs avec un taux d'apprentissage de 0,4. La Table 5 illustre les résultats afin d'intervenir pour un examen clinique, GBM envoie environ une fausse alerte toutes les 3 semaines. Cependant, il est moins sensible que le NN. Le compromis spécificité/sensibilité doit

Table 5 -

 5 Résultats de la classification binaire pour chaque classificateur

	Classifieur Sensibilité Spécificité Précision
	NN	92.88%	94.18%	93.51%
	SVM	77.96%	90.91%	84.21%
	KNN	76.61%	93.45%	84.73%
	RF	88.47%	94.54%	91.41%
	GBM	89.15%	95.27%	92.1%
	être trouvé en fonction du diagnostic médical.
	Bien que NN, RF et GBM constituent un système d'alerte précis pour les cliniciens au quo-
	tidien (précision supérieure à 91%), le taux de fausses alertes reste globalement relativement
	élevé. La fréquence du diagnostic (durée entre deux décisions différentes) peut affecter les per-
	formances des systèmes prédictifs. Une analyse à long terme pourrait être plus appropriée pour
	ce type de caractéristiques. Par conséquent, nous avons considéré un intervalle plus long, à sa-
	voir 5 jours. L'idée est de garder le concept d'une prédiction quotidienne, mais en envoyant une
	seule notification en se basant sur la prédiction la plus fréquente sur les 5 derniers jours. Par
	exemple, si le système prédit que le sujet est robuste 4 fois sur 5, alors la décision finale sur ces
	5 jours considérera le sujet comme étant en bonne santé (sans envoyer une alerte un jour sur
	cinq). Ainsi, la sensibilité du NN a atteint 98,25% et sa spécificité 98,08%. Ces résultats sou-
	lignent l'importance de cibler une étude longitudinale pour ce type de mesures. Une évolution
	défavorable au niveau de ces cinq caractéristiques globales sur des périodes significativement
	plus longues semble être la base de la prévention de la fragilité.

Table 6 -

 6 Résultats des différents classifieurs alimentés par les paramètres de marche proposés

	Classifieur	NN	SVM	KNN	DT	RF	GBM
	Précision (%) 88.18% 88.5% 86.26% 85.42% 87.26% 87.51%

vue de Robust 92.3% 11.3% 8.7%

	la prévention de la fragilité. Les dispositifs portables sont préférés aux capteurs externes pour ABSTRACT
	diverses raisons. Par conséquent, le premier type a été utilisé pour atteindre l'objectif de cette
	étude. Par suite, le système à considérer se compose de deux modules, à savoir (i) le module de
	détection des activités physiques, et (ii) le module d'analyse de la fragilité, qui analyse les ADLs
	détectées pour évaluer la condition physique du sujet. Tout au long de cette thèse, plusieurs
	contributions ont été apportées pour réaliser le système ciblé. En particulier, (a) une revue des This work mainly focuses on activity monitoring of elderly with a view to frailty analysis. This
	différents outils méthodologiques de surveillance a été effectuée, afin de choisir les composants geriatric syndrome, represented by physiological weakening and sarcopenia, would affect 4 out of
	de notre système, (b) deux bases de données ont été créées, à savoir FallAllD et ActFreeLi, pour 5 people over 85 years old in France. With the absence of a gold standard, self-reported measures,
	développer les techniques nécessaires et les valider, (c) une solution sophistiquée pour les trackers questionnaires, and some other performance tests have been proposed to assess the wellness of
	portés au poignet a été proposée, qui cible les ADLs cycliques et les périodes d'inactivité, (d) older adults. Frailty has been operationally defined by Fried et al. as meeting three out of five
	une approche à haute complexité basée sur un capteur MARG (placé sur le tronc) a été proposée criteria: unintentional weight loss, low physical activity, low grip strength, exhaustion, and slowed
	pour une reconnaissance plus spécifique des activités, étant donné que les dispositifs portés au gait. Three stages were defined, namely robust (healthy), pre-frail (heading towards frailty),
	poignet ne sont pas suffisants pour l'analyse de la fragilité, (e) une autre technique à faible and frail. The aforementioned data being subjective and measured over short-term evaluation
	coût basée sur l'accélération (le capteur étant placé sur le tronc) a également été proposée under supervised conditions, we propose a wearable sensor-based fully automated monitoring
	comme solution alternative pour les systèmes embarqués, (f) des variables globales d'activité system to cope with these issues. It consists of two separate layers: (1) a machine learning-based
	ont été définies, basées sur la sortie du module de la détection des activités, pour caractériser human activity recognition (HAR) module to detect Activities of Daily Living (ADLs), and (2)
	la fonction physique des personnes âgées et détecter sa détérioration, et (g) une unité d'analyse a second module to analyze the localized ADLs. Two HAR approaches were developed. The
	de la marche pour étudier la relation entre la façon dont les personnes âgées marchent et leur first one is a complex architecture, based on the orientation of a MARG (Magnetic, Angular
	condition physique a été développée. Rate, Gravity) sensing unit, combining both handcrafted features and automatically learned
	En prolongement de ce travail, il conviendrait de s'orienter principalement suivant quatre features by Convolutional Neural Networks (CNN) and recurrent Long Short-Term Memory
	axes. Premièrement, les techniques développées pourraient être testées sur des bases de données (LSTM) networks. A second embeddable solution is also proposed. It is a low-cost acceleration-
	Nous avons constaté que le développement de systèmes de surveillance, basés sur des objets plus larges et sur des durées plus longues afin d'affiner les paramètres pour augmenter la fiabilité based recognition process, exploiting local temporal characteristics of segmented signals with few
	du système et d'observer des trajectoires. Deuxièmement, l'état psycho-cognitif pourrait être pris en compte dans l'évaluation des conditions de fragilité. En d'autres termes, un module de traitement du langage naturel pourrait être développé pour analyser le discours des personnes âgées, ce qui pourrait révéler leur état de fragilité d'une autre manière. En troisième lieu, l'état de fragilité pourrait alors être évalué en combinant (1) des données cliniques telles que le poids, la tension et la fréquence cardiaque, (2) des données liées à l'activité physique (déjà proposées floating point operations per second. Experimental results on several public datasets prove the efficiency of our techniques, which outperform state-of-the-art methods. Now, once localized, the ADLs represented by windowed time-series feed the second module. Here, two types of activity and health metrics are considered to analyze and assess the health conditions of elderly: (a) global features, computed over the course of the day, and (b) local features, computed over local segments (related to a specific activity). Experimental results, using data of community-dwelling connectés, est nécessaire pour détecter automatiquement l'affaiblissement physique en Pre-frail 5% 86.6% dans cette thèse) et (3) des données liées à l'état psycho-cognitif. Finalement, la capacité à elderly in free-living conditions, are correlated with frailty phenotype and constitute useful clues 8.4% prédire l'aggravation physique future sur différentes échelles temporelles pourrait être étudiée, in the frailty trajectory. The feasibility and efficiency of this monitoring system being proved,
	avec comme objectif la prédiction de l'état de fragilité dans le futur (détection précoce de la the development of a product is now conceivable, and its combination with natural language
	Frail fragilité) plutôt que la simple détection de l'état actuel. 2.7% 2.1% processing and clinical data to predict a future physical worsening will be an extension of the 82.9% present work.
	Robust	Pre-frail	Frail
	Figure 11 -Matrice de confusion résultant du classifieur SVM.

TABLE OF CONTENTS Acronyms List of Figures List of Tables Introduction 1 Background and Problem Statement 1

  .1 Frailty Syndrome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Identification and Assessment: Related Work . . . . . . . . . . . . . . . . . . . . 1.3 Fall Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Limitations and Drawbacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

	1.5.1 Wearable Sensor-based Monitoring . . . . . . . . . . . . . . . . . . . . . .
	1.5.2 Human Activity Recognition . . . . . . . . . . . . . . . . . . . . . . . . .
	1.5.3 Physical Weakening Identification . . . . . . . . . . . . . . . . . . . . . .
	1.5.4 Evaluation using Different Experimental Settings . . . . . . . . . . . . . .

2 Choice of the Telemonitoring Solution

  Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

	2.1 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	2.2 Sensor Placement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	2.3 Processing Units and Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	2.3.1 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	2.3.2 Attitude Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	2.3.3 Feature Extraction and Classification Process . . . . . . . . . . . . . . . .
	2.4 Design of Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	2.4.1 FallAllD for Activity Recognition . . . . . . . . . . . . . . . . . . . . . . .
	2.4.1.1 Devices and Characteristics . . . . . . . . . . . . . . . . . . . . .
	2.4.1.2 Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	2.4.2 ActFreeLi for Frailty Analysis . . . . . . . . . . . . . . . . . . . . . . . . .
	2.4.2.1 Devices and Characteristics . . . . . . . . . . . . . . . . . . . . .
	2.4.2.2

Appendices A Sample of Questionnaires and Performance Tests B Quaternions and Attitude Estimation C Computational Complexity D FallAllD Characteristics E Up-Down Acceleration Pattern F Customized Transfer Function G MDA Computational Complexity Bibliography List of Publications ACRONYMS

  Organizational chart justifying the choice of the considered classes for wrist-worn tracker. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F s = G F s = 60 Hz and M F s = 40 Hz. . . . . . . . . . . . . . . . . . . . . . . . . are updated as indicated in the figure. . . . . . . . . . . . . . . . . . . . . . . . . 3.17 The 5L extracted features using online computation. . . . . . . . . . . . . . . . .

	HAR Human Activity Recognition IMU Inertial Measurement Unit SPPB Short Physical Performance Battery SVM Support Vector Machine 3.3 3.4 Proposed peak detection technique: a λ (j) satisfying Eq. (3.1) (red crosses) and LIST OF FIGURES
	IQR Interquartile Range TUG Timed Up and Go the actual peaks (black circles). . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	3.5 Feature extraction. (a) Prominence (red) and width (green) of the second peak
	ADLs Activities of Daily Living KNN k-Nearest Neighbors ZOI Zone Of Interference 1 Flow diagram illustrating the elements of ACCORDS project. . . . . . . . . . . . in an acceleration signal. (b) Dx segments for class C-1 (left) and class C-4 (right).
	3.6 Data distribution. (a) The 2D distribution of activities following the first two
	AHRS Attitude and Heading Reference System LDA Linear Discriminant Analysis 1.1 The different stages of frailty model with aging curves as a function of age, namely features (Prominence vs Width). (b) The SVM L hyperplane in 3D space (C-2 vs
	AQUA Algebraic QUaternion Algorithm normal aging and accelerated aging. . . . . . . . . . . . . . . . . . . . . . . . . . C-3) after adding a third feature (Entropy) and its intersection with the (Entropy, LSTM Long-Short Term Memory 1.2 Frailty cycle (Fried et al., 2001; Fried et al., 2003): (a) its simplified version in Width) 2D plane. (c) The SVM Q hyperplane in 3D space (C-1 vs C-4) after adding
	AUC Area Under Curve blue and (b) the frailty phenotype criteria. . . . . . . . . . . . . . . . . . . . . . . a third feature (Variability). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MARG Magnetic, Angular Rate, Gravity 1.3 Biomarkers for frailty screening and analysis. . . . . . . . . . . . . . . . . . . . . 3.7 Proposed machine learning architecture for wrist-worn tracker to classify recurrent BERT Bidirectional Encoder Representations from Transformers MDA Multinomial Decomposition Algorithm 1.4 The three components (a X , a Y , a Z ) of an acceleration signal representing the movements into four different classes. . . . . . . . . . . . . . . . . . . . . . . . . .
	CDL CNN, Dense, LSTM different phases of a forward fall while walking caused by a slip. . . . . . . . . . . 3.8 Confusion matrix of the proposed model for wrist-worn device using a 10-fold MEMS Micro-Electro-Mechanical Systems 1.5 The human gait cycle, with the corresponding stance and swing phases which cross validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	CFS Clinical Frailty Scale NB Naive Bayes constitute around 60% and 40% of the cycle respectively. This is a simplified 3.9 Acquisition cycle when (i) all modalities have the same sampling rate (configura-
	NLP Natural Language Processing et al., 2015). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CNN Convolutional Neural Network version of the functional divisions of the gait cycle originally published in (Stöckel tion λ 1 ) and (ii) the magnetometer has a lower rate (configuration λ 2 ), particularly
	NN Neural Network 1.6 Flow diagram of the present work, where activity monitoring is divided into three 3.10 Initial position of the wearable sensor (at t = 0) symbolized by a parallelepiped DGI Dynamic Gait Index main steps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . with vertices V i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	DNN Deep Neural Network DoF Degree of Freedom DT Decision Tree PCA Principal Component Analysis 3.11 Wearable sensor orientation when the subject is walking (left graph), when the 2.1 Accelerometers vs Gyroscopes in terms of consumed current (extracted from (Q. Liu et al., 2017)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . human body is hitting the ground during the impact phase of the fall (right graph). PCB Printed Circuit Board 3.12 The proposed HAR mechanism, consisting of two deep learning networks (CNN 2.2 Recordings of acceleration signals acquired from six different body locations (ex-PEC PiezoElectriC tracted from (Cleland et al., 2013)). . . . . . . . . . . . . . . . . . . . . . . . . . & LSTM) and a fully connected network (dense layers). . . . . . . . . . . . . . .
	EKF Extended Kalman Filter 2.3 Recordings of acceleration signals resulting from four activities, using a wrist-worn 3.13 Confusion matrix (showing the rates in %) of (a) the 9-class model and (b) the PSQI Pittsburgh Sleep Quality Index accelerometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-class model after combining C 5 and C 6 into one class C 5 . . . . . . . . . . . . .
	QDA Quadratic Discriminant Analysis 2.4 The barometric pressure as (i) raw signal (green), (ii) slope-limited signal (or-3.14 Organizational chart showing the possible movements of an elderly from a trunk-FeFu Feature Fusion ange), and (iii) moving average output (blue). . . . . . . . . . . . . . . . . . . . . placed device point of view. The blue leaves represent the targeted ADLs and the
	flops floating-point operations per second RBF Radial Basis Function 2.5 Device attitude. (a) The device frame (D) and the Earth frame (E). (b) The red leaves represent the activities to be excluded. . . . . . . . . . . . . . . . . . .
	FPU Floating-Point Unit 3.15 Acceleration signals representing stand-to-sit and sit-to-stand transitions (dark orientation of the device frame (D) relative to Earth frame (E) in terms of Euler RF Random Forest angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . blue): two opposite sine waves in magnitude ||a||. The a Z component, directed
	FrI Frailty Index RNN Recurrent Neural Network towards the human trunk, fluctuates during these two transitions. . . . . . . . . 2.6 The printed circuit board with the corresponding components. . . . . . . . . . . 3.16 Online computation technique consisting of m buffers ζ [i] of length n. The red
	FrP Frailty Phenotype RS Random Subspace 3.1 Acceleration signals {a X , a Y , a Z } captured from the human body trunk and arrows indicate the propagation of acquired data-points. For each new read value
	GBM Gradient Boosting Machine 3.2 Magnitude ||a|| of acceleration signals resulting from "Jogging" and "Walking" SAE Stacked AutoEncoder representing the targeted ADLs. . . . . . . . . . . . . . . . . . . . . . . . . . . . ν, the ζ [i] j values are shifted by one sample, ζ [1] 1 is excluded, and the elements χ i
	GRU Gated Recurrent Unit SD Standard Deviation respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A

Table 2 .

 2 1 -MEMS vs PEC accelerometers following different attributes

	Attribute	MEMS (I) PEC (II)	Comment
	Low cost		(II) difficult to mass-produce
	Low power consumption		Signals of (II) need amplification
	High temperature		Up to 350 • C
	High frequency range		> 500 Hz
	High impact shock		> 200 g units
	Non-sensitive to humidity
	Static acceleration
	worth mentioning that PEC accelerometers are difficult to mass-produce, while MEMS ones are

available for much lower prices, while having a lower power consumption. More importantly, the latter type not only measures the linear acceleration caused by the body movement but also the pseudo-acceleration caused by gravity (static acceleration), since it can be imagined as a mass suspended on two sides with springs

Table 2 .

 2 2 -Experimental results comparing the computational load of orientation filters in terms of execution time (s) required for orientation estimation approaches. Besides, other approaches have been proposed to estimate the orientation. Mahony et al.[START_REF] Mahony | Nonlinear complementary filters on the special orthogonal group[END_REF] proposed an algorithm which employs a nonlinear complementary filter. Fourati et al.[START_REF] Fourati | A nonlinear filtering approach for the attitude and dynamic body acceleration estimation based on inertial and magnetic sensors: bio-logging application[END_REF] combined a quaternion-based nonlinear filter with the Levenberg Marquardt Algorithm. The Algebraic QUaternion Algorithm (AQUA) has been also discussed[START_REF] Pierleoni | A wearable fall detector for elderly people based on ahrs and barometric sensor[END_REF]. In 2011,Madgwick et al. proposed a computationally efficient MARG orientation filter[START_REF] Madgwick | Estimation of imu and marg orientation using a gradient descent algorithm[END_REF], based on an optimised gradient descent algorithm. It exploits quaternion representation.

	Orientation Filter EKF Mahony Madgwick AQUA Fourati
	Time (s)	1.03	0.28	0.17	0.26	0.82
	low latency is

  Hence, another deep learning module is added. It consists of a CNN and takes acceleration signals as input.CNN models usually deal with image classification problems, since they exploit the spatial correlation in data. Thus, they are appropriate to capture the shape of acceleration time-series.These signals are re-arranged to constitute an activity image of size (6F s × 3). With F s = 60 Hz, each column accounts for one component of 360-point length (i.e. 6 s × 60 Hz). This model is defined by five convolutional layers, consisting of 16, 32, 64, 128, and 256 filters respectively.

Table 3 .

 3 1 -Experimental results comparing HAR techniques in terms of accuracy (%)

	Classifier	CNN	LSTM	CDL	KNN	DNN	RF	RS
	Input	Raw data Raw data	Both	Features Features Features Features
	Accuracy (9-class)	92.81%	76.71%	97.7%	90.85%	86.12%	89.31%	76.13%
	Accuracy (8-class)	94.25%	78.15%	98.68% 92.54%	89.67%	92.23%	77.31%

Sitting down -𝑪′ 𝟐 : Standing up -𝑪′ 𝟑 : Lying down -𝑪′ 𝟒 : Rising up 𝑪′ 𝟓 : Walking -𝑪′ 𝟔 : Jogging -𝑪′ 𝟕 : Inactive -𝑪′ 𝟖 : Others

	𝑪 𝟏 97.04 2.24	0.13	0	0.21	0.76	0	0.21	0.4
	𝑪 𝟐 2.07 97.07	0		0	0		0.96	0	0.1	0.39
	𝑪 𝟑	0	0	99.48 0.78	0		0		0	0	0
	𝑪 𝟒	0	0	0.26 99.22	0		0		0	0.32	0
	𝑪 𝟓 0.06	0.13	0		0	98.19 5.79	0	0	0
	𝑪 𝟔 0.25	0.06	0		0	1.5	91.73	0	0	0.13
	𝑪 𝟕	0	0	0		0	0		0.57	100	0	0
	𝑪 𝟖 0.13	0.06	0		0	0		0		0	99.37	0
	𝑪 𝟗 0.45	0.44	0.13	0	0.1	0.19	0	0	99.08
		𝑪 𝟏	𝑪 𝟐	𝑪 𝟑		𝑪 𝟒	𝑪 𝟓	𝑪 𝟔		𝑪 𝟕	𝑪 𝟖	𝑪 𝟗
		𝑪′ 𝟐 1.16 98.15 𝑪′ 𝟑 0.06 0 𝑪′ 𝟒 0 0 𝑪′ 𝟓 0.22 0.12 𝑪′ 𝟔 0 0 𝑪′ 𝟕 0.12 0.12 𝑪′ 𝟖 0.31 0.25 𝑪′ 𝑪′ 𝟏 98.13 1.36 𝑪′ 𝟏 𝑪′ 𝟐	0 0 99.08 0.52 0 0 0.92 99.11 0 0 0 0 0 0 0 0.37 𝑪′ 𝟑 𝑪′ 𝟒	0.41 0.07 0 0 99.24 0.13 0 0.15 𝑪′ 𝟓	0 0 0 0 0.2 99.8 0 0 𝑪′ 𝟔	0.1 0 0 0 0 0 99.8 0.1 𝑪′ 𝟕	0.59 0.52 0.06 0.2 0.25 0 0 98.38 𝑪′ 𝟖

𝟏 :

Table 3 .

 3 2 -Results of DL methods when trained and tested on the same data

	Model	CNN	RNN	LSTM	GRU	SAE
	Results 96.89% 45.21% 83.31% 97.37% 97.82%
	Yang et al., 2008):

Table 3 .

 3 3 -Accuracy using a 10-fold cross validation on FallAllD

	Classifier Learning	Input	Accuracy
	MDA	Shallow	F 1,...,5L	98.03%
	CCS	Shallow	F 1,...,5L	95%
	CNN	Deep	Raw Data	96.72%
	SAE	Deep	Raw Data	90.8%
	GRU	Deep	Raw Data	95.96%
	NN	Shallow	HFeats	91.26%
	SVM	Shallow	HFeats	94.44%
	KNN	Shallow	HFeats	99%
	RF	Shallow	HFeats	95.82%
	GBM	Shallow	HFeats	99.27%
	DT	Shallow	HFeats	91.01%
	NB	Shallow	HFeats	75%
	LDA	Shallow	HFeats	83.4%
	QDA	Shallow	HFeats	89.51%
	FeFu	Fusion	Raw data + HFeats	96.84%

  .4 -Characteristics of five public datasets in terms of employed accelerometers, sampling frequency F s , and placement of the device the characteristics of these datasets. This strategy is able to reveal the identity of overfitted models, since the classifiers are trained on a particular dataset, then evaluated on other datasets with different participants, sensing units, configurations, and protocols of clinical trials. Consequently, the seven targeted ADLs (C 1 , ..., C 7 ) were considered to see if the trained classifiers are able to identify them accurately when tested on a new dataset. 3 windows were

	Dataset Accelerometer	F s	Placement Postural Transitions
	FallAllD	LSM9DS1	238 Hz Neck, Waist	Yes
	SisFall	ADXL345	200 Hz	Waist	Yes
	mHealth	Shimmer2	50 Hz	Chest	No
	HAPT	Galaxy S2	50 Hz	Waist	Yes
	UMAFall	MPU-9250	20 Hz Chest, Waist	Yes
	3.4 displays

Table 3 .

 3 6 -Time (in s) for training, feature extraction and prediction MDA that is equal to Ξ = 12d + 11k + 30 flops (where d and k are the length of the feature vector and the number of output classes respectively). Let us give a numerical example. Suppose that L = 5. In this case, based on section 3.3.2.4 (seeFigures 3.17

	Method Training Feature Extraction + Prediction
	MDA	15.12 s	0.173 s
	CNN	34.16 s	2.54 s
	SAE	10.46 s	0.55 s
	GBM	107.13 s	23.018 s
	KNN	0.55 s	24.235 s
	GRU	4909.2 s	26.12 s
	LSTM	4991.3 s	29.17 s
	FeFu	4965.4 s	26.22 s

Table 4 .

 4 2). Let us indicate that MET values that are greater than 6 are not considered in our context. Therefore, the number of burned calories C i resulting from the i th activity is estimated

Table 4 .

 4 2 -MET equivalents depending on activity class and intensity , and the eighth feature G 8 is an approximation of EE over the course of the day, and is computed as:

	State	Type & Intensity	MET
	Inactive		-	1
		Light Movements	1.5 -1.8
			Low	2
	Active	Cyclic	Moderate Brisk	3.3 5
			Jogging	> 6
			126

Table 4 .

 4 3 -Different statistics representing the extracted health measurements of (a) frail people and (b) healthy (non-frail) old people

		Features Steps	Activity Rate *	Periodicity Rate * T p †	CIA † † Lift Stairs	SE *	EE ‡
		mean	1019	14.5	0.23	1.9	0.98	0.02	75.4	20.7
		(±SD)	(±939)	(±4.8)	(±0.3)	(±0.63)	(±1.04)	(±0.06)	(±10.5)	(±2)
	Frail	Q1	397	11.5	0	1.5	0.1	0	74.8	19.3
		Q3	1895	18.9	0.45	2.25	1.38	0.01	80.6	22.1
		mean	4663	20	3.5	1.18	1.58	1.41	88.2	26.6
		(±SD)	(±2036)	(±5.7)	(±5)	(±0.04)	(±1.7)	(±1.12)	(±10.7)	(±2.3)
	Healthy	Q1	2819	14.9	1.2	1.14	0.46	0.8	76.5
		Q3	6658	23.5	2.6	1.22	2.64	1.8	96.6

Table 4 .

 4  of each feature using Wilcoxon rank sum test . Generally, robust older adults are more active as seen in Table

	Feature	Steps	Activity Rate	EE	SE Periodicity	Stairs	Lift	T p
	p-value < 0.001	NS	< 0.001 NS	< 0.001	< 0.001 NS < 0.001
	NS: Not Significant
	the stairs, and T

p

Table 4 .

 4 5 -Binary classification results for each classifier (daily prediction)

	Classifier Sensitivity Specificity Accuracy
	NN	92.88%	94.18%	93.51%
	SVM	77.96%	90.91%	84.21%
	KNN	76.61%	93.45%	84.73%
	RF	88.47%	94.54%	91.41%
	GBM	89.15%	95.27%	92.1%
	frail is considered the positive class. The feature vectors fed five machine learning classifiers of
	different types, namely NN of 1 hidden layer of 15 neurons with a sigmoidal activation function,
	SVM with RBF kernel, KNN with k = 5, RF of 10 estimators and a maximum depth equal to 5,
	and GBM of 100 estimators with a learning rate of 0.4. Leave-Subject-Out (LSO) cross-validation
	was applied, i.e. the classifier was trained on 17 subjects, then tested on the remaining one 18
	times. The overall positives and negatives of these predictions were counted to evaluate the
	specificity, sensitivity, and accuracy using true positive (TP), false positive (FP), true negative
	(TN), and false negative (FN) values:

Table 4 .

 4 6 -Binary classification results for each classifier following a 5-day prediction

	Prediction		Averaging			Voting
	Classifier	RF	NN	GBM	RF	NN	GBM
	Sensitivity 73.68% 78.95% 73.68% 96.49% 98.25% 91.23%
	Specificity 96.15% 92.31% 96.15% 98.08% 98.08% 98.08%
	Accuracy	84.4% 85.32% 84.4%	97.25% 98.17% 94.5%

  These features are able to separate the initial state (robust/healthy elderly) from the final state (frail/vulnerable elderly). Their evolution over time (relatively long periods) is a key to detect progressive physical worsening. In the remainder of this chapter, local features (calculated over local segments), which may reflect the damage in physical function, are proposed.

	Sen = 97.89%
	Spe = 97.72%
	Acc = 97.81%	Sen = 100%
	Sen = 98.25% Spe = 98.08%	Spe = 100% Acc = 100%
	Acc = 98.17%
	Sen = 92.88%
	Spe = 94.18%
	Acc = 93.51%

  3, a new set of features can be extracted for gait analysis. Those gait parameters are referred to as local features since they are extracted from local segments, containing acceleration signals of older adults while walking. While longitudinal study is required to analyze global features, a cross-sectional study is needed for local ones. In other words, we need to analyze data from one population at a specific point in time. While global features like the number of steps might vary significantly over small periods as previously mentioned, the gait parameters characterize the manner of walking at a particular moment, and thus reflect the physical capacities of the person at this moment.

Table 4 .

 4 7 -Individual performance in terms of balanced accuracy (%) and p-value of the Kruskal-Wallis test for the six gait parameters The aforementioned features vary in unit, range and magnitude. Hence, they are scaled using the sigmoidal function (Eq. (

	Gait Parameter	Component Accuracy † p-value*
	F 1 : intensity of movements (trimmed range)	||a||	73.2%	< 0.001
	F 2 : cadence (steps/s)	||a||	66.8%	< 0.001
	F 3 : periodicity (autocorrelation)	||a||	61.4%	< 0.001
	F 4 : variability (pNN)	||a||	72.9%	< 0.001
	F 5 : σ φ (AR Model)	a X	61.9%	< 0.001
	F 6 : K φ (AR Model)	a X	58.1%	< 0.001
	† 10-fold cross validated balanced accuracy
	* Kruskal-Wallis test
	frail, and frail.

Table 4 .

 4 8 -Results of different machine learning classifiers fed by the proposed gait parameters

	Classifier	NN	SVM Q SVM R	KNN	DT	RF	GBM
	Accuracy (%) 88.18% 86.85% 88.5% 86.26% 85.42% 87.26% 87.51%
	data). The achieved accuracy in this case does not reveal the reliability of the system in real
	world situations.

  Let us assume that t p , t pr , and t f are three different time slots, namely past, present, and future respectively. Moreover, suppose that H p , H pr , and H t are the corresponding states of the older adult at each time slot. Now, the goal is to predict the Grip strength: the strength is measured by a dynamometer (in Kg). Subjects who do not exceed the following cut-off values are considered frail by this criterion:

	Men	Cut-off (time to walk)
	Height ≤ 173 cm	≥ 7 seconds
	Height > 173 cm	≥ 6 seconds
	Women	Cut-off (time to walk)
	Height ≤ 159 cm	≥ 7 seconds
	Height > 159 cm	≥ 6 seconds
	• Men	Cut-off (grip strength)
	BMI ≤ 24	≥ 29 Kg
	BMI 24.1-28	≥ 30 Kg
	BMI > 28	≥ 32 Kg
	Women	Cut-off (grip strength)
	BMI ≤ 23	≥ 17 Kg
	BMI 23.1-26	≥ 17.3 Kg
	BMI 26.1-29	≥ 18 Kg
	BMI > 29	≥ 21 Kg

  dz sinθ 2 ] and ⊗ the quaternion product. Consequently, Euler angles describe this orientation achieved by sequential rotations of ψ around z E , θ around y E , and φ around x E

			3)
	with: D E q = [cos θ 2	-dx sin θ 2	-dy sin θ 2

  • M. Abbas, D. Somme and R. Le Bouquin Jeannès, "Identifying Physical Worsening in Elderly Using Objective and Self-Reported Measures," 2021 Sixth International Conference on Advances in Biomedical Engineering (ICABME), 2021, pp. 193-196. → doi: 10.1109/ICABME53305.2021.9604819. • M. Abbas, D. Somme and R. Le Bouquin Jeannès, "Machine Learning-Based Physical Activity Tracking with a view to Frailty Analysis," 2020 42nd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), 2020, pp.

	3917-3920.

  Résumé : Caractérisée par un affaiblissement de la fonction physique, la fragilité toucherait, en France, 4 personnes âgées sur 5 de 85 ans et plus. Dans ce contexte, afin de suivre l'activité physique des seniors et d'analyser leur trajectoire de fragilisation, nos travaux ont consisté à proposer un système de surveillance automatisé basé sur des capteurs portables. Ce système se compose de deux couches distinctes, un premier module d'apprentissage automatique pour identifier les activités physiques et un second pour analyser la sortie précédente. Concernant le premier module, deux approches ont été développées. La première, complexe en temps de calculs, considère en entrée des signaux acquis par un accéléromètre, un gyroscope et un magnétomètre, et est basée sur l'orientation du dispositif portable, combinant à la fois un processus d'extraction manuelle de caractéristiques et des réseaux de deep learning. La seconde, peu coûteuse et pouvant être embarquée, exploite des caractéristiques temporelles locales des seuls signaux d'accélération. Une fois ces signaux labellisés, ils viennent alimenter le second module. Deux types de mesures de l'activité sont alors extraits des données étiquetées pour évaluer l'état de santé des personnes âgées, à savoir des variables globales calculées au cours d'une journée, et des variables locales caractérisant la démarche. Une étude longitudinale sur des données acquises en conditions non supervisées au cours de la vie quotidienne de sujets âgés (robustes, préfragiles et fragiles) a permis d'attester l'efficacité et la faisabilité de notre solution.

Title: Detecting and analyzing physical activity in older adults using wearable sensors towards frailty trajectory assessment Keywords: detection, classification, physiological signals, sensors, physical activity, health monitoring

+ exp(-2x)

ACKNOWLEDGMENTS

This work was carried out at Laboratoire Traitement du Signal et de l'Image (LTSI), in Rennes, France, and was supported by the French National Research Agency in the context of the ACCORDS project (grant n • ANR-17-CE19-0024-01). Before you start reading this thesis, it is important for me to thank some people, without whom nothing could have been done.

I owe my deepest gratitude to my supervisor at the University of Rennes 1, Régine Le Bouquin Jeannès. Her continuous support, her expertise, and her advice have been precious to

arrows. However, there is no such segment/interval in the yellow window when the subject is walking. All data-points exceed 0.6 g. Let us indicate that the illustrated patterns appear when the subject performs the aforementioned activities while wearing a device on his body trunk.

They are like a signature to these ADLs. However, this is not the case for wrist-worn devices.

The subject may walk with free hands, or may walk while rolling a stroller or while holding a baby for example. The patterns are not the same when captured from the wrist. The same goes for transient ADLs, because the movements of the arm are not always the same, and might resemble other activities. These observations and remarks are important when it comes to the proposal of a recognition system (described in the following sections).

Wrist-worn Tracker

As mentioned in the previous chapter, the Silver@Home project tackled fall detection. Two positions were considered, namely wrist-worn and necklace devices, seeing that they accompany the subject anywhere even under the shower and in bed. This is important since a fall detector must be able to track the elderly continuously and ensure a timely intervention. The wrist-worn device was considered as one of the best in terms of acceptability in this context, and thus we opted for it in the first instance. Now, as previously discussed, wrist movements could be complex since the arm moves with high DoFs. The shape of acquired signals might change even when performing the same activity, which could mislead the recognition system and lead to erroneous results. Moreover, activities like sitting down, standing up, lying down, and rising up (postural transitions) are not well captured by wrist-worn devices, since the arm is not fixed to the body. Therefore, a sophisticated approach is needed for wrist-worn trackers with decent reliability. Accordingly, an acceleration-based recognition technique is proposed (Abbas and Le Bouquin Jeannès, 2020). It localizes recurrent movements and inactivity periods while excluding transient movements.

Proposed Strategy

The logic behind this approach relies on the fact that the movements of a subject are classified into three main categories that are cyclic activities, transient activities and inactivity (no movement). Cyclic activities, acquired by a wrist-worn device, are typified by recurrent movements of the wrist/arm. Now, the subject can move his arm in two cases: (i) his body is idle or (ii) his body is moving. The activities of the first scenario could be divided into two families: (i-1) activities resulting from constant shocks/hits of the hand (like clapping) and (i-2) activities requiring hand-waving. Three families result from scenario (ii): (ii-1) going forward without leaving the floor (walking, going upstairs and downstairs), (ii-2) going forward rapidly while leaving the ground for a short while (jogging or running) and (ii-3) going forward while floating (swimming).

where V is an acceleration time-series of length n, and V i its i-th element. Since the standard deviation is proportional to the power of the signal, it quantifies the movements intensity. These two variables, when computed globally over the window as a whole (from end to end), determine the statistical patterns of a signal. Now, to encode the temporal structures of the windowed data, we computed these two features over local segments. Specifically, a X and a Z are divided into equal non-overlapping sub-segments of 1-second length to calculate their mean values. Mean-

Transitions Recurrent

Sitting down

Others

Standing up Others

Walking Jogging S1 S2

S3

Figure 3.18 -Proposed multinomial decomposition algorithm, consisting of three stages S1 → S3, which predicts the performed activity at a low-cost.

complexity. Indeed, after being experimentally tested using parallel loops, it was shown that the logarithm operation is almost 25 times more complex than a multiplication. Finally, the output layer consists of a linear function.

Classification by stage: as mentioned earlier in this section, MDA converts the organizational chart of Figure 3.14 into a tree-like structure classification process. It is illustrated, in its optimized form, in Figure For both methods, a decision is taken every second. Thanks to a developed mobile application or a computer software (a future product), the user can display the performed ADLs instantaneously. The first method is executed on a remote server (pc or tablet for example),

where the application/software is already installed. The second one can be embedded in wearable devices and executed on a micro-controller. In this case, the wearable device is connected to an electronic device (mobile phone for example) to send the label of the predicted activity, where the application is already installed. Now, if a decision is made every second, a total of 86400 predictions are done in 24 hours. With 98% accuracy (which is quite high), 1728 windows are misclassified if we want to consider the activity of each sliding window. However, the goal of a HAR system in real world conditions is the accurate localization of ADLs (postural transitions and cyclic movements) for an ideal post-processing, and not blind recognition.

Therefore, to ensure a robust output, the application/software applies a voting technique on the last three outputs after each prediction. The result of this operation is displayed on the screen.

For example, if {Walking, Jogging, Walking, Walking, Sitting down, Sitting down} is the list of decisions: are first calculated in free-living conditions using data of ActFreeLi, then statistically tested in unsupervised conditions to characterize the different populations. The discrimination power of the most discriminant features is investigated next, using a group of machine learning classifiers detecting the frailty conditions of a person (indicated by FrP). Finally, a graphical representation of the proposed activity metrics is provided as a tool to assist clinicians and improve their diagnosis.

Global Activity Measurements

Feature Extraction

Based on the output of the previous module, illustrated in Figure 3.22 (HAR module detailed in the previous chapter), several variables, referred to as global features, are proposed. These features are calculated over the course of a day (24 hours). It is worth mentioning that the number of rows in the re-arranged output, i.e. right table in Figure 3.22.b, is variable (depending on the performed ADLs by the wearer of the device). For instance, if the subject is sitting the whole time during the observation period (i.e. while he is wearing the device), this table will consist of one row (the activity class being "Inactive"). Nonetheless, the total duration is 24 hours in the case of global features, regardless of the number of rows in the table (i.e. the number of performed ADLs). respectively. Now, when the subject is inactive or slightly moving and the slope is varying considerably (in the range of 0.6-0.9 m/s for example), the corresponding window is relabeled as "lift". Meanwhile, when the subject is walking and the altitude is rising/decreasing moderately (0.25 ≤ | tan(θ)| ≤ 0.6), the corresponding window is relabeled as "climbing/descending stairs".

𝜃 𝐿 𝜃 𝑆

Suppose that 1 L (i) is an indicator function that is equal to 1 if the i th activity (i th row of the table in Figure 3.22) is labeled as "lift" and 0 otherwise. Meanwhile, 1 S (i) is an indicator function a) b)

Movements Intensity Cadence

Periodicity Variability (AR Model) (AR Model) Hence, the proposed method classifies them as robust, which raises the confusion rate between classes. Besides, the confusion matrix should be carefully interpreted. Although the off-diagonal elements represent the rate of misclassified signals, a part of this confusion between different output classes is informative and valuable for the analysis of the syndrome, and is not the result of the system deficiency. In fact, the Robust/Pre-frail and Pre-frail/Frail misclassification rates might be crucial to detect the weakening of the person, and define the curvature of frailty trajectory. It is true that those 5% of robust subjects, which are classified as pre-frail by the model, are considered as being robust by FrP at this particular moment. Nevertheless, those older adults might very well tend to become pre-frail and are likely to be considered as such by the aforementioned phenotype in the next few weeks. This finding is important for prevention and could help the practitioner and suggest him to intervene in order to avoid serious consequences resulting from this sickness. The same remark holds for the 2.1% confusion between Frail and Pre-frail classes. As for the 8.4% confusion rate, the interpretation is quite the opposite. The gait of seniors, who are frail according to Fried's criteria, is still not completely damaged. In such a situation, the role of the physician is still essential to help the older adult in retrieving his physical condition and avoid any sudden turn towards disability. In summary, this section assessed the discrimination power of a novel set of gait parameters and its ability to predict the frailty status automatically while assessing and detecting the transition towards frailty. Our results are twofold: (i) the resultant confusion matrix is well correlated with frailty phenotype, (ii) the deviations from the target classes should be seen as important and useful clues in the frailty trajectory. future status (at t f ) based on (i) the current state (t pr ) or (ii) the difference between the current and past states (t pr -t p ) using the predefined multimodal system. To the best of our knowledge, predicting a future worsening has received little attention in the literature.

This might be a valuable contribution in the analysis of frailty trajectory.

Appendix A

SAMPLE OF QUESTIONNAIRES AND PERFORMANCE TESTS

This appendix gives an example of questionnaires and performance tests which are used in clinical settings to evaluate the physical condition of older adults and define frailty.

Frailty Phenotype (FrP)

Five criteria are used to define the frailty status of the subject, as indicated in [START_REF] Fried | Frailty in older adults: evidence for a phenotype[END_REF].

• Weight loss: K = (weight in previous year -current weight)/(weight in previous year).

If K≥0.05 and the subject does not report an intentional weight loss, then he/she is considered frail for weight loss.

• Exhaustion: two statements are read: (i) "I felt that everything I did was an effort" and (ii) "I could not get going." Afterwards, the following question is asked: "How often in the last week did you feel this way?"

Four answers are possible: 0 = rarely or none of the time (<1 day); 1 = some or a little of the time (1-2 days); 2 = a moderate amount of the time (3-4 days); 3 = most of the time. By answering "2" or "3" to either of these two questions, the subject is considered frail by this criterion.

• Physical activity: the subject is asked about walking, raking, gardening, hiking, jogging, dancing, swimming etc, based on the short version of the Minnesota Leisure Time Activity questionnaire. Kcals per week are calculated using standardized algorithm.

Men with less than 383 Kcals per week are considered frail by this criterion.

Women with less than 270 Kcals per week are considered frail by this criterion.

• Walk time: time to walk 15 feet is measured (in seconds). Subjects exceeding the following cut-off values are considered frail by this criterion:

Side-by-side • Gait speed test: the participant has to perform a 4-meter walk with his usual pace (two attempts are possible). The following score is assigned, depending on the performance: "0" if the test is impossible for the subject, "1" if time exceeds 8.70 seconds, "2" if time is 6.21 to 8.70 seconds, "3" if time is 4.82 to 6.20 seconds, "4" if time is less than 4.82 seconds.

Semi-tandem Tandem

Note that the shortest time is used to calculate the score.

• Chair stand test: the participant has to stand up then sit down for five times as quickly as he/she can, while keeping his/her arms folded across the chest. The following score is assigned, depending on the performance: "0" if unable to complete the task or if time exceeds 60 seconds, "1" if time exceeds 16.70 seconds, "2" if time is 13.70 to 16.69 seconds, "3" if time is 11.20 to 13.69 seconds, "4" if time is less than 11.19 seconds.

The final score is the sum of three points above (points of each test). The higher the score, the healthier the subject is.

QUATERNIONS AND ATTITUDE ESTIMATION

Quaternions are a 4-dimensional extension of the complex numbers [START_REF] Kuipers | Quaternions and rotation sequences: a primer with applications to orbits, aerospace and virtual reality[END_REF]. They can represent the orientation of a body in a three-dimensional space, and produce a 3D rotation.

A quaternion q is equal to a + bi + cj + dk, where i, j, k are fundamental quaternion units.

a is called the real part and the rest (bi + cj + dk) is called the vector part. The conjugate q is equal to q after multiplying the vector part by -1. The multiplication rules regarding this representation are as follows:

Two fundamental units being multiplied together do not commute, since one is the negation of the other.

To describe an orientation, the quaternion should be of unit length: q o = cos(α)+sin(α)(r x i+ r y j + r z k), assuming that r x 2 + r y 2 + r z 2 = 1. Three observations can be noted:

• by left-multiplying every point in the space by q o , we rotate two circles, namely (a) the one passing by 1 and r x i + r y j + r z k, and (b) the one perpendicular to it (these two circles are orthogonal).

• by left-multiplying every point by qo , we rotate these two circles in opposite directions.

• by right-multiplying by qo , we only negate the rotation direction of circle (a).

Hence, left-multiplying by q o and right-multiplying by qo will cancel rotation (a) while doubling rotation (b) (rotation by 2α). Now, let us project these representations to our actual situation (attitude of a wearable sensor relative to Earth frame). F D denotes the device frame while F E that of the earth. Suppose that a certain point of this body is represented by a three dimensional vector ϑ. Moreover, a certain

COMPUTATIONAL COMPLEXITY

The following operations are taken into consideration: addition and subtraction α, comparison ς, multiplication β, division γ, multiply-and-accumulate β (one operation), logarithm and exponential Λ. Note that: (a) the "sign" and "array indexing" are free operations at the machine level, (b) comparison is nothing but subtraction without storing the result and (c) the final result will be simplified and written as a function of some reference parameter ϕ (1 flops) to which the operations will be related.

DT compares the features to some predefined threshold until a leaf is reached. Thus, the involved computations are Ξ DT = w n ς, with w n indicating the number of accessed nodes.

SVM classifies the feature vector F as follows [START_REF] Cristianini | An introduction to support vector machines and other kernel-based learning methods[END_REF][START_REF] Hastie | The elements of statistical learning[END_REF]:

where Ψ( F ) is defined by:

with ν i = [ν i1 , ..., ν iN ] T ∀i = 1, ..., S being the support vectors, S the number of support vectors, N the length of feature vector, κ a kernel function (defined below), ŵi the weights and b 0 the bias. For linear kernels (SVM L ) and quadratic kernels (SVM Q ), the equations are the following ones:

with a being a constant. Therefore, the corresponding outputs are: Therefore, the complexity is equal to Ξ KN N = M (N (α + β) + kς).

For numerical application, let us suppose that we have a matrix of size 1000 × 10 (i.e. 1000 samples and 10 features). Moreover, we have α = ς β = β γ = ϕ = 1 flops (FPU single precision). Ξ DT does not depend on N and/or M , but it is linked to the number of nodes in the tree. For deep trees (for example a depth of 100), and for k = 3 (3-NN), the computational complexity of each classifier is:

This justifies why memory-based classifiers are not convenient for embedded algorithms.

FALLALLD CHARACTERISTICS

The simulations were executed by 15 subjects (8 males and 7 females). Their ages, weights and heights range from 21 to 53 years, 48 to 85 kg, and 158 to 187 cm respectively. The average age, weight and height are 32 years, 67 kg and 171 cm respectively. As recommended in [START_REF] Noury | A proposal for the classification and evaluation of fall detectors[END_REF], each subject selected the devices that are convenient for him/her, and simulated the activities and/or falls he/she accepted to do. Table D.1 illustrates the devices worn by each participant and the number of falls and/or ADLs that he/she simulated.

The total number of simulations (of 20 s length each) is equal to 6605 (the sum of Falls and ADLs in Table D.1). Each of these simulations is represented by 4 files, containing acceleration data, angular velocity, magnetic fields, and barometric pressure respectively. Hence, the total number of files is 4 × 6605 = 26420. Now, each of these files is named as 'Sa_Db_Ac_Td_S'.

S indicates the subject's ID (a = 01, 02, ..., 15), D indicates the number of the wearable device

UP-DOWN ACCELERATION PATTERN

Let us assume that MEMS accelerometers are equivalent to an ideal case of single spring and single mass system without any force opposing the motion of the components as illustrated in Appendix F

CUSTOMIZED TRANSFER FUNCTION

The Taylor series for exponential exp(u) (where u > 0) is:

The hyperbolic tangent sigmoid transfer function h(x) is:

By replacing exp(u) by 1 + u (order 1) in h(x) we obtain the customized transfer function h (x):

MDA COMPUTATIONAL COMPLEXITY

The computational complexity of one stage of MDA (i.e. the use of a NN to make a prediction) is now calculated in flops.

The NN begins by scaling the feature vector F of length d using the min-max normalization:

This step requires ξ 1 = dα + dβ operations.

Afterwards, F constitutes the input of the hidden layer (fully-connected) of 10 neurons. Hence, it is transformed as follows:

where M and B h are of size 10 × d and 10 × 1 respectively. This step results in ξ 2 = 10d β + 10α operations. Subsequently, the customized transfer function h (x) is applied on F , resulting in F as output while involving ξ 2 = 10α + 10β operations.

Finally, F feeds the output layer to finalize the k-class classification process: