Alexis Joly

Hervé Goëau

Stefan Kahl

Benjamin Deneu

Maximillien

Lukáš

Rafael Ruiz De Castañeda

Isabelle Bolon

Andrew Durso

Christophe Botella

Ivan Eggel

Willem-Pier Vellinga

Pierre Bonnet

Henning Müller

Overview of LifeCLEF 2020: a System-oriented Evaluation of Automated Species Identification and Species Distribution Prediction

Building accurate knowledge of the identity, the geographic distribution and the evolution of species is essential for the sustainable development of humanity, as well as for biodiversity conservation. However, the difficulty of identifying plants and animals in the field is hindering the aggregation of new data and knowledge. Identifying and naming living plants or animals is almost impossible for the general public and is often difficult even for professionals and naturalists. Bridging this gap is a key step towards enabling effective biodiversity monitoring systems. The LifeCLEF campaign, presented in this paper, has been promoting and evaluating advances in this domain since 2011. The 2020 edition proposes four data-oriented challenges related to the identification and prediction of biodiversity: (i) PlantCLEF: cross-domain plant identification based on herbarium sheets, (ii) BirdCLEF: bird species recognition in audio soundscapes, (iii) GeoLifeCLEF: location-based prediction of species based on environmental and occurrence data, and (iv) SnakeCLEF: snake identification based on image and geographic location.

LifeCLEF Lab Overview

Accurately identifying organisms observed in the wild is an essential step in ecological studies. Unfortunately, observing and identifying living organisms requires high levels of expertise. For instance, plants alone account for more than 400,000 different species and the distinctions between them can be quite subtle. Since the Rio Conference of 1992, this taxonomic gap has been recognized as one of the major obstacles to the global implementation of the Convention on Biological Diversity 14 . In 2004, Gaston and O'Neill [START_REF] Gaston | Automated species identification: why not?[END_REF] discussed the potential of automated approaches for species identification. They suggested that, if the scientific community were able to (i) produce large training datasets, (ii) precisely evaluate error rates, (iii) scale up automated approaches, and (iv) detect novel species, then it would be possible to develop a generic automated species identification system that would open up new vistas for research in biology and related fields.

Since the publication of [START_REF] Gaston | Automated species identification: why not?[END_REF], automated species identification has been studied in many contexts [START_REF] Cai | Sensor network for the monitoring of ecosystem: Bird species recognition[END_REF][START_REF] Trifa | Automated species recognition of antbirds in a mexican rainforest using hidden markov models[END_REF][START_REF] Towsey | A toolbox for animal call recognition[END_REF][START_REF] Glotin | Proc. 1st workshop on Machine Learning for Bioacoustics -ICML4B. ICML[END_REF][START_REF]NIPS Int. Conf.: Proc. Neural Information Processing Scaled for Bioacoustics, from Neurons to Big Data[END_REF][START_REF] Lee | Contour matching for a fish recognition and migration-monitoring system[END_REF][START_REF] Joly | Interactive plant identification based on social image data[END_REF][START_REF] Yu | Automated identification of animal species in camera trap images[END_REF]. This area continues to expand rapidly, particularly due to recent advances in deep learning [START_REF] Ghazi | Plant identification using deep neural networks via optimization of transfer learning parameters[END_REF][START_REF] Lee | Multi-organ plant classification based on convolutional and recurrent neural networks[END_REF][START_REF] Bonnet | Plant identification: experts vs. machines in the era of deep learning[END_REF][START_REF] Wäldchen | Automated plant species identification-trends and future directions[END_REF][START_REF] Wäldchen | Machine learning for image based species identification[END_REF][START_REF] Van Horn | The inaturalist species classification and detection dataset[END_REF]. In order to measure progress in a sustainable and repeatable way, the Life-CLEF 15 research platform was created in 2014 as a continuation and extension of the plant identification task [START_REF] Goëau | The imageclef plant identification task[END_REF] that had been run within the ImageCLEF lab 16 since 2011 [START_REF] Goëau | The imageclef 2011 plant images classification task[END_REF][START_REF] Goëau | Imageclef2012 plant images identification task[END_REF][START_REF] Goëau | The imageclef 2013 plant identification task[END_REF]. Since 2014, LifeCLEF expanded the challenge by considering animals in addition to plants, and including audio and video content in addition to images [START_REF] Joly | LifeCLEF 2014: Multimedia Life Species Identification Challenges[END_REF][START_REF] Joly | Lifeclef 2015: multimedia life species identification challenges[END_REF][START_REF] Joly | LifeCLEF 2016: Multimedia Life Species Identification Challenges[END_REF][START_REF] Joly | LifeCLEF 2017 Lab Overview: Multimedia Species Identification Challenges[END_REF][START_REF] Joly | Overview of LifeCLEF 2018: a large-scale evaluation of species identification and recommendation algorithms in the era of ai[END_REF][START_REF] Joly | Overview of LifeCLEF 2019: Identification of Amazonian Plants, South & North American Birds, and Niche Prediction[END_REF]. Four challenges were evaluated in the context of LifeCLEF 2020 edition: 1. PlantCLEF 2020: Identifying plant pictures from herbarium sheets. 2. BirdCLEF 2020: Bird species recognition in audio soundscapes. [START_REF] Bolon | Identifying the snake: First scoping review on practices of communities and healthcare providers confronted with snakebite across the world[END_REF]. GeoLifeCLEF 2020: Species distribution prediction based on occurrence data, environmental data and remote sensing data. 4. SnakeCLEF 2020: Automated snake species identification based on images and two level geographic location data -continent and country.

The system used to run the challenges (registration, submission, leaderboard, etc.) was the AICrowd platform 17 . About 172 researchers or students registered to at least one of the four challenges of the lab and 16 of them finally crossed the finish line by completing runs and participating in the collaborative evaluation. In the following sections, we provide a synthesis of the methodology and main results of each of the four challenges of LifeCLEF2020. More details can be found in the overview reports of each challenge and the individual reports of the participants (references provided below).

PlantCLEF challenge: Identifying plant pictures from herbarium sheets

A detailed description of the task and a more complete discussion of the results can be found in the dedicated working note [START_REF] Goëau | Overview of lifeclef plant identification task[END_REF].

Objective

Automated identification of plants has recently improved considerably thanks to the progress of deep learning and the availability of training data with more and more photos in the field. For instance, we measured in 2018 a top-1 classification accuracy over 10K species up to 90 % and we showed that automated systems are not so far from human expertise [START_REF] Joly | Overview of LifeCLEF 2018: a large-scale evaluation of species identification and recommendation algorithms in the era of ai[END_REF]. However, this profusion of field images only concerns a few tens of thousands of species, mostly located in North America and Western Europe, with fewer images from the richest regions in terms of biodiversity such as tropical countries. On the other hand, for several centuries, botanists have collected, catalogued and systematically stored plant specimens in herbaria, particularly in tropical regions. Recent huge efforts by the biodiversity informatics community such as iDigBio 18 or e-ReColNat 19 made it possible to put millions of digitized collections online. In the continuity of the PlantCLEF challenges organized in previous years [START_REF] Goëau | The imageclef 2011 plant images classification task[END_REF][START_REF] Goëau | Imageclef2012 plant images identification task[END_REF][START_REF] Goëau | The imageclef 2013 plant identification task[END_REF][START_REF] Goëau | The lifeclef 2014 plant images identification task[END_REF][START_REF] Goëau | Lifeclef plant identification task[END_REF][START_REF] Goëau | Plant identification in an open-world (lifeclef 2016)[END_REF][START_REF] Goëau | Plant identification based on noisy web data: the amazing performance of deep learning (lifeclef 2017)[END_REF][START_REF] Goëau | Overview of expertlifeclef 2018: how far automated identification systems are from the best experts ?[END_REF][START_REF] Goëau | Overview of lifeclef plant identification task 2019: diving into data deficient tropical countries[END_REF], this year's challenge was designed to evaluate to what extent automated plant species identification on tropical data deficient regions can be improved by the use of herbarium sheets. Herbaria collections represent potentially a large pool of data to train species prediction models, but they also introduce a difficult and interesting problem of cross domain classification because typically a same plant photographed in the field takes on a different visual appearance when dried and placed on a herbarium sheet as it can be seen in figure 1.

Dataset and Evaluation Protocol

The challenge is based on a dataset of 997 species mainly focused on the South America's Guiana Shield (figure 2), an area known to have one of the greatest diversity of plants in the world. The challenge was evaluated as a cross-domain classification task where the training set consist of 321,270 herbarium sheets and 6,316 photos in the field to enable learning a mapping between the two domains.

A valuable asset of this training set is that a set of 354 plant observations are provided with both herbarium sheets and field photos to potentially allow a more precise mapping between the two domains. The test set relied on two highly trusted experts and was composed of 3,186 photos in the field related to 638 plant observations. Participants were allowed to use complementary training data (e.g. for pretraining purposes) but on the condition that (i) the experiment is entirely reproducible, i.e. that the used external resource is clearly referenced and accessible Fig. 1: Field photos and herbarium sheets of the same specimen (Tapirira guianensis Aubl.). Despite the very different visual appearances between the two types of images, similar structures and shapes of flowers, fruits and leaves can be observed.

to any other research group in the world, (ii) the use of external training data or not is mentioned for each run, and (iii) the additional resource does not contain any of the test observations. External training data was allowed but participants had to provide at least one submission that used only the training data provided this year.

The main evaluation measure for the challenge was the Mean Reciprocal Rank (MRR), which is defined as

1 Q Q q=1 1 rank q
where Q is the number of plant observations and rank q is the predicted rank of the true label for the qth observation.

A second metric was again the MRR but computed on a subset of observations of species that are rarely photographed in the field. The species were chosen based on the most comprehensive estimates possible from different data sources (IdigBio, GBIF, Encyclopedia of Life, Bing and Google Image search engines, previous datasets related to PlantCLEF and ExpertCLEF challenges). It is therefore a more challenging metric because it focuses on the species which impose a mapping between herbarium and field photos.

Participants and Results

68 participants registered for the PlantCLEF challenge 2020 (PC20) and downloaded the data set, and 7 research groups succeeded in submitting runs, i.e. files containing the predictions of the system(s) they ran. Details of the methods and systems used in the runs are synthesized in the overview working note paper of the task [START_REF] Goëau | Overview of lifeclef plant identification task[END_REF] and further developed in the individual working notes of most of the participants (Holmes [START_REF] Chulif | Herbarium-field triplets network for cross-domain plant identification -neuon submission to lifeclef 2020 plant[END_REF], ITCR PlantNet [START_REF] Villacis | Domain adaptation in the context of herbarium collections: a submission to plantclef 2020[END_REF], SSN [START_REF] Nanda H Krishna | Plant species identification using transfer learning -plantclef 2020[END_REF], LU [START_REF] Zhang | Adversarial consistent learning on partial domain adaptation of plantclef 2020 challenge[END_REF]). The remaining teams did not provide an extended description of their systems but Fig. 2: Density grid maps of the number of species of geolocated plants in Plant-CLEF2020. Many species have also been collected to a lesser extent in other regions outside French Guiana, such as the Americas and Africa. sometimes a few informal descriptions were provided in the metadata associated with the submissions and partially contributed to the comments below. We report in Figure 3 the performance achieved by the 49 collected runs. The most difficult plant challenge ever. This year's challenge is confirmed to be the most difficult of all previous editions, with at best a quite low MRR value of 0.18. As already noticed last year, tropical flora is inherently more difficult than the generalist flora explored during the previous eight years, even for experts [START_REF] Goëau | Overview of lifeclef plant identification task 2019: diving into data deficient tropical countries[END_REF]. The asymmetry between training data based on herbarium sheets and test data based on field photos did not make the task any easier.

Traditional CNNs performed poorly. Figure 3 shows a great disparity between the performance obtained by the different submissions. To explain that we have first to distinguish between approaches based on CNNs alone (typically pretrained on ImageNet and finetuned with the provided training data) and approaches that additionally incorporate an explicit and formal Domain Adaptation (DA) technique between the herbarium and field domains. As expected regarding the low number of field photos in the training set for numerous species, directly finetuned CNNs with the PC20 data obtained the lowest scores (ITCR Run 1, SSN Run 1&2, UWB Run 1).

External training data on traditional CNNs did not really improve performances. CNNs can be improved by the use of external data, involving more field photos, as it is demonstrated with the UWB runs 2 & 3 and ITCR Run 2. All these runs extended the training data with the previous year's PC19 training data and the GBIF training data provided by [START_REF] Picek | Recognition of the amazonian flora by inception networks with test-time class prior estimation[END_REF]). ITCR Run 2 made a greater improvement on the overall MRR probably by using a two stage training strategy: they first finetuned an ImageNet-pretrained ResNet50 with all the herbarium sheets from PC20, and then finetuned it again with all the field photos extracted from PC20 and the external training data. This two stages strategy can be seen as a naive DA technique because the second stage shifts the learned features in an initial herbarium feature space to a field photo feature space. However, regarding the second MRR metric focusing on the most difficult species with few field photos in the training set, performance for all these runs is still quite low. This means that the performance of a traditional CNN approach (without a more formal adaptation technique) is too dependent from the number of field photos available in the training data, and is not able to efficiently transfer visual knowledge from herbarium domain to field photos domain.

Adversarial DA techniques performed the best. Among other submissions, two participants stood out from the crowd with two quite different DA techniques. ITCR PlantNet team based all its remaining runs on a Few Shot Adversarial Domain Adaptation approach [START_REF] Motiian | Few-shot adversarial domain adaptation[END_REF] (FSADA), directly applied in the run 3. FSADA approach uses a discriminator that helps the initial encoder trained on herbarium sheets to shift the learned feature representations to a domain agnostic feature space where the discriminator is no longer able to distinguish if a picture comes from the herbarium or the photo domain, while maintaining the discriminative power regarding the final species classification task. The basic FSADA approach (ITCR Run 3) clearly outperformed the traditional CNN approach (run 1), while both approaches are based on the same initial finetuned ResNet50 model on the PC20 training herbarium data. It should be noted that the LU team also used an adversarial approach but with less success.

Mapping DA technique reached an impressive genericity on difficult species. While the adversarial DA technique used by the ITCR PlantNet team obtained the best result on the main MRR metric, the Neuon AI team obtained the best results on the second MRR metric focusing on the most difficult species in the test set. This last team used two encoders, one trained on the herbarium sheets in PC20 and a second one trained on the photos from the PC17 dataset. Then they learned a distance function based on a triplet loss to maximize the embedding distance of different species and at the same time minimize the distance of the same species. Performances measured from the Neuon AI Run 5, which is an ensemble of 3 instances of their initial approach, gave especially impressive results with quite high MRRs and above all similar values between the two MRR metrics. It means that Neuon AI's approach is very robust to the lack of training field photos and able to generalize on rare difficult species in the test set. In other words, their approach is able to transfer knowledge to rare species which was the underlying objective of the challenge.

External data improved DA approaches. ICTR Run 4 shows a significant impact on the main MRR metric from using external training data compared to the same adversarial DA approach (run 3), while maintaining the same level of genericity on rare species with similar MRRs value on the second metric. Unfortunately it is not possible to measure this impact on the Neuon AI method because they did not provide a run using only this year's training data.

Auxiliary tasks have impact, notably by the use of upper taxon level information in a multi classification task way integrated to the FSADA approach (ITCR Run 6 is better than run 4 with a single species classification task). This is the first time over all the years of PlantCLEF challenges that we clearly observe an important impact of the use of genus and family information to improve the species identification. Many species with few training data have apparently been able to benefit indirectly from a "sibling" species with many data related to a same genus or family. The impact is probably enhanced this year because of the lack of visual data on many species. To a lesser extent, self supervision auxiliary task such as jigsaw solving prediction task (ITCR Run 5 improved a little the baseline of this team (run 4), and the best submission over all this year challenge is an ensemble of all FSADA approaches, combining self supervision or not, upper taxons or not.

BirdCLEF challenge: Bird sound recognition in complex acoustic environments

A detailed description of the task and a more complete discussion of the results can be found in the dedicated overview paper [START_REF] Kahl | Overview of birdclef 2020: Bird sound recognition in complex acoustic environments[END_REF].

Objective

The LifeCLEF Bird Recognition Challenge (BirdCLEF) launched in 2014 and has since become the largest bird sound recognition challenge in terms of dataset size and species diversity with multiple tens of thousands of recordings covering up to 1,500 species [START_REF] Goëau | Overview of birdclef 2018: monophone vs. soundscape bird identification[END_REF], [START_REF] Kahl | Overview of birdclef 2019: Large-scale bird recognition in soundscapes[END_REF]. Birds are ideal indicators to identify early warning signs of habitat changes that are likely to affect many other species. They have been shown to respond to various environmental changes over many spatial scales. Large collections of (avian) audio data are an excellent resource to conduct research that can help to deal with environmental challenges of our time.

The community platform Xeno-canto20 launched in 2005 and hosts bird sounds from all continents and daily receives new recordings from some of the remotest places on Earth. The Xeno-canto archive currently consists of more than 550,000 recordings covering over 10,000 species of birds, making it one of the most comprehensive collections of bird sound recordings worldwide, and certainly the most comprehensive collection shared under Creative Commons licenses. Xeno-canto data was used for BirdCLEF in all past editions to provide researchers with large and diverse datasets for training and testing. The diversity of this data made BirdCLEF a demanding competition and required participating research groups to develop efficient processing and classification pipelines. The large number of recordings often forced participants to reduce the training data and the number of features-strongly implying the deficiencies of low-level audio feature classification for extremely large datasets. In 2016, Sprengel et al. applied the classical scheme of image classification with deep neural networks to the domain of acoustic event recognition and introduced a convolutional neural network (CNN) classifier trained on extracted spectrograms that instantly outperformed all previous systems by a significant margin [START_REF] Sprengel | Audio based bird species identification using deep learning techniques[END_REF]. The success of deep neural networks in the domain of sound identification led to the disappearance of MFCCs, SVMs and decision trees which dominated previous editions.

Despite their success for bird sound recognition in focal recordings, the classification performance of CNN on continuous, omnidirectional soundscapes remained low. Passive acoustic monitoring can be a valuable sampling tool for habitat assessments and the observation of environmental niches which often are endangered. However, manual processing of large collections of soundscape data is not desirable and automated attempts can help to advance this process. Yet, the lack of suitable validation and test data prevented the development of reliable techniques to solve this task. This changed in 2019 when 350 hours of fully annotated soundscapes were introduced as test data. Participants were asked to design a detection system that was trained on focal recordings (provided by the Xeno-canto community) and applied to hour-long soundscapes. Bridging the acoustic gap between high-quality training recordings and soundscapes with high ambient noise levels is one of the most challenging tasks in the domain of audio event recognition.

Dataset and Evaluation Protocol

Deploying a bird sound recognition system to a new recording and observation site requires classifiers that generalize well across different acoustic domains. Focal recordings of bird species from around the world form an excellent base to develop such a detection system. However, the lack of annotated soundscape data for a new deployment site poses a significant challenge. As in previous editions, training data was provided by the Xeno-canto community and consisted of more than 70,000 recordings covering 960 species from three continents (South and North America and Europe). Participants were allowed to use this and other (meta) data to develop their systems. A representative validation dataset with two hours of soundscape data was also provided, but participants were not allowed to use this data for training-detection systems had to be trained on focal recordings only.

In addition to the 2019 test data, soundscapes from three other recording sites were added in the 2020 edition of BirdCLEF. All audio data were collected with passive acoustic recorders from deployments in Germany (GER), Peru (PER), the High Sierra Nevada (HSN) of California, USA and the Sapsucker Woods area (SSW) in New York, USA. In an attempt to lower the entry level of this challenge, the total amount of soundscape data was reduced to 153 recordings with a duration of ten minutes each. Expert ornithologists provided annotations for often extremely dense acoustic scenes with up to eight species vocalizing at the same time (1.9 on average, see Figure 4).

The goal of the task was to localize and identify all audible birds within the provided soundscape test set. Each soundscape was divided into segments of 5 seconds, and a list of species associated to probability scores had to be returned for each segment. The used evaluation metric was the classification mean Average Precision (cmAP ), considering each class c of the ground truth as a query. This means that for each class c, all predictions with ClassId = c are extracted from the run file and ranked by decreasing probability in order to compute the average precision for that class. The mean across all classes is Fig. 5: Scores achieved by all systems evaluated within the bird identification task of LifeCLEF 2020. computed as the main evaluation metric. More formally:

cmAP = C c=1 AveP (c) C
where C is the number of classes (species) in the ground truth and AveP (c) is the average precision for a given species c computed as:

AveP (c) = nc k=1 P (k) × rel(k) n rel (c) .
where k is the rank of an item in the list of the predicted segments containing c, n c is the total number of predicted segments containing c, P (k) is the precision at cut-off k in the list, rel(k) is an indicator function equaling 1 if the segment at rank k is a relevant one (i.e. is labeled as containing c in the ground truth) and n rel (c) is the total number of relevant segments for class c.

Participants and Results

69 participants registered for the BirdCLEF 2020 challenge and downloaded the dataset. Four teams succeeded in submitting runs. Details of the methods and systems used in the runs are synthesized in the overview working notes paper of the task [START_REF] Kahl | Overview of birdclef 2020: Bird sound recognition in complex acoustic environments[END_REF] and further developed in the individual working notes of the participants ([1], [START_REF] Clementino | Using triplet loss to bird species recognition on birdclef 2020[END_REF]). In Figure 5 we report the performance achieved by the 13 collected runs.

All submitted runs featured a CNN classifier trained on extracted audio features and all approaches employ current best practices from past editions.

Established neural network architectures like VGG, Inception v3, EfficientNet, Xception, or the baseline repository [START_REF] Kahl | Recognizing birds from sound -the 2018 birdclef baseline system[END_REF] were used in the majority of the submitted runs. Most attempts used log-scale spectrograms as input, only one team used a custom Gabor wavelet layer in their network design. All participants used pre-processed data and distinguished between salient audio chunks and noise (i.e. non-events) to improve the performance of their classifier. Data augmentation is key for generalization and all participating research groups used a set of domainspecific augmentation methods. The results reflect the slight imbalance of the test data in terms of number of soundscapes per recording site and individual vocalization density. The highest scoring team achieved a class-wise mean average precision of 0.128 across all four recording sites (0.148 on validation data). Some of the participating groups did not manage to score above a cmAP of 0.01 which highlights the demanding nature of this task despite the versatility of deep neural networks. This becomes even more apparent when investigating the classification performance for the South American split of the test data. The highest scoring system achieved a cmAP of only 0.07, on average, the cmAP across all submission was 0.017 for this portion of the test set. Participants scored best for soundscapes recorded in North America with a maximum score of 0.333 for the High Sierra Nevada data. Species composition and recording characteristics play a significant role and the detection quality highly depends on avian call density. Additionally, significant improvements of current classifiers are needed to develop a reliable bird sound recognition system for highly endangered habitats in South America. Current training regimes and neural network architectures might not be suited for this task.

GeoLifeCLEF challenge: species distribution prediction based on occurrence data, environmental data and remote sensing data

A detailed description of the task and a more complete discussion of the results can be found in the dedicated working note [START_REF] Deneu | Overview of LifeCLEF location-based species prediction task 2020 (GeoLifeCLEF)[END_REF].

Objective

Automatic prediction of the list of species most likely to be observed at a given location is useful for many scenarios related to biodiversity management and conservation. First, it could improve species identification tools (whether automatic, semi-automatic or based on traditional field guides) by reducing the list of candidate species observable at a given site. More generally, it could facilitate biodiversity inventories through the development of location-based recommendation services (e.g. on mobile phones), encourage the involvement of citizen scientist observers, and accelerate the annotation and validation of species observations to produce large, high-quality data sets. Last but not least, this could be used for educational purposes through biodiversity discovery applications with features such as contextualized educational pathways.

Data Set and Evaluation Protocol

Data collection: A detailed description of the GeoLifeCLEF 2020 dataset is provided in [START_REF] Cole | The GeoLifeCLEF 2020 dataset[END_REF]. In a nutshell, it consists of over 1.9 million observations in US and France covering 31, 435 plant and animal species (as illustrated in Figure 7). Each species observation is paired with high-resolution covariates (RGB-IR imagery, land cover and altitude) as illustrated in Figure 6. These high-resolution covariates are resampled to a spatial resolution of 1 meter per pixel and provided as 256 × 256 images covering a 256m × 256m square centered on each observation. RGB-IR imagery come from the 2009-2011 cycle of the National Agriculture Imagery Program (NAIP) for the U.S. 21 , and from the BD-ORTHO® 2.0 and ORTHO-HR® 1.0 databases from the IGN for France 22 . Land cover data originates from the National Land Cover Database (NLCD) [START_REF] Homer | Completion of the 2011 national land cover database for the conterminous united states -representing a decade of land cover change information[END_REF] for the U.S. and from CESBIO 23 for France. All elevation data comes from the NASA Shuttle Radar Topography Mission (SRTM) 24 . In addition, the dataset also includes traditional coarser resolution covariates: bio-climatic rasters (1km 2 /pixel, from WorldClim [START_REF] Hijmans | Very high resolution interpolated climate surfaces for global land areas[END_REF]) and pedologic rasters (250m 2 /pixel, from SoilGrids [START_REF] Hengl | Soilgrids250m: Global gridded soil information based on machine learning[END_REF]).

Train-test split: The full set of occurrences was split in a training and testing set using a spatial block holdout procedure (see Figure 7). This limits the effect of spatial auto-correlation in the data as explained in [START_REF] Roberts | Crossvalidation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure[END_REF]. This means that a model cannot achieve a high performance by simply interpolating between training samples. The split was based on a global grid of 5 km × 5 km quadrats. 2.5% of the quadrats were randomly sampled for the test set, and the remaining quadrats were assigned to the training set.

Evaluation metric: For each occurrence in the test set, the goal of the task was to return a candidate set of species with associated confidence scores. The main evaluation criterion is an adaptive variant of the top-K accuracy. Contrary to a classical top-K accuracy, this metric assumes that the number of species K may not be the same at each location. It is computed by thresholding the confidence score of the predictions and keeping only the species above that threshold. The threshold is determined automatically so as to have K = 30 results per occurrence on average. See [START_REF] Cole | The GeoLifeCLEF 2020 dataset[END_REF] for full details and justification.

Participants and Results

40 participants registered for the GeoLifeCLEF 2020 challenge and downloaded the dataset. Only two of them succeeded in submitting runs: Stanford and LIRMM. A major hindrance to participation was the volume of data as well as the computing power needed to train the models (e.g. almost two weeks to train a convolutional neural network on 8 GPUs). Details of the methods and systems Fig. 6: Each species observation is paired with high-resolution covariates (clockwise from top left: RGB imagery, IR imagery, altitude, land cover). used in the runs of both participants are synthesized in the overview working note paper for this task [START_REF] Deneu | Overview of LifeCLEF location-based species prediction task 2020 (GeoLifeCLEF)[END_REF]. Runs of the LIRMM team are further developed in the individual working note [START_REF] Deneu | Participation of LIRMM / Inria to the Geo-LifeCLEF 2020 challenge[END_REF]. Due to convergence issues for runs of Stanford team, after discussion with the authors, it was mutually agreed that they would not provide additional working notes for their runs.

In Figure 8 we report the performance achieved by the 9 collected runs 25 . The main outcome of the challenge was that the method achieving the best results (LIRMM/Inria Run 3) was based solely on a convolutional neural network (CNN) trained on the high-resolution covariates (RGB-IR imagery, land cover, and altitude). It did not make use of any bioclimatic variable or soil type variable whereas these variables are often considered as the most informative in the ecological literature. On the contrary, the method used in LIRMM/Inria Run 1 was based solely on the punctual environmental variables using a machine learning method classically used for species distribution models (Random Forest, [START_REF] Evans | Modeling species distribution and change using random forest[END_REF]). This shows two things: (i) important information explaining the species composition is contained in the high-resolution covariates and (ii), convolutional neural networks are able to capture this information. An important following question would be to know whether the information captured by the high-resolution CNN is complementary to the one captured from the bioclimatic and soil variables. This was the purpose of LIRMM/Inria Run 4 that merged the prediction of both models by averaging their outputs. Unfortunately, this was not really conclusive. Either the high-resolution CNN already captured most of the information contained in the bioclimatic variables, or the fusion method was not able to take the best of each model.

5 SnakeCLEF challenge: Automated snake species identification based on images and two-level geographic location data (continent and country).

A detailed description of the task and a more complete discussion of the results can be found in the dedicated overview paper [START_REF] Picek | Overview of the snakeclef 2020: Automatic snake species identification challenge[END_REF].

Objective

To create an automatic and robust system for snake species identification is an important goal for biodiversity, conservation, and global health. With over half a million victims of death and disability from venomous snakebite annually, having a system that is capable to recognize or differentiate various snake species from images could significantly improve eco-epidemiological data and treatment outcomes (e.g. based on specific use of antivenoms) [START_REF] De Castañeda | Snakebite and snake identification: empowering neglected communities and health-care providers with ai[END_REF][START_REF] Bolon | Identifying the snake: First scoping review on practices of communities and healthcare providers confronted with snakebite across the world[END_REF]. Since snake species identification is a fine-grained visual categorization task, the main difficulty of this challenge is the high intra-class and low inter-class variances. In other words, certain classes could be highly variable in appearance depending on geographic location, sex, or age (Figure 9) and at the same time could be visually similar to other species (e.g. mimicry) (Figure 10). The goals and usage of image-based snake identification are complementary with those of other challenges: classifying snake species in images and predicting the list of species that are the most likely to be observed at a given location.

Dataset and Evaluation Protocol

Dataset Overview: For this challenge we have prepared a dataset with 259,214 images belonging to 783 snake species from 145 countries. The dataset has a heavy long-tailed class distribution, where the most frequent species (Thamnophis sirtalis) is represented by 12,201 images and the least frequent by just 17 (Naja pallida). Such a distribution with small inter-class variance and high intra-class Testing Dataset: Apart from other LifeCLEF challenges, the final testing set remains undisclosed as it is a composition of private images from individual reporters and natural history museums who have not put those images online in any form. A brief description of this closure method is as follows -twice as big as the validation set, contains all 973 classes, and observations from almost all the countries presented in training and validation sets.

Geographical Information: For approximately 80% of the images we provided a two levels of geographical information -country and continent. We have collected observations across 145 countries and all continents. Such information could be crucial for the AI based recognition as it is useful for human experts. Evaluation: The main goal of this challenge was to build a system that is autonomously able of recognizing 973 snake species based on the given image and geographical location input. Every participant had to submit their whole solution into the GitLab based evaluation system that performed evaluation over the secret testing set. Since data were secret each participated team could submit up to 5 submissions per day. The main evaluation metric for this challenge was the Dice Similarity Coefficient (DSC), also known as F1 score. This metric considers the uncertainty of a given prediction based on how much it differs from the actual label. This gives us a more subtle evaluation of the performance.

Participants and Results

Out of 8 registered teams in the SnakeCLEF 2020 challenge, only 2 teams managed to submit a working version of their recognition system. Even though participants were able to evaluate their system 5 times a day, we have registered only 27 submissions. Details of the methods and systems used in the runs are synthesized in the overview working note paper of the task [START_REF] Picek | Overview of the snakeclef 2020: Automatic snake species identification challenge[END_REF] and further developed in the individual working notes (FHDO BCSG [START_REF] Bloch | Combination of image and location information for snake species identification using object detection and efficientnets[END_REF]], Gokuleloop [START_REF] Moorthy | Impact of pretrained networks for snake species classification[END_REF]). In a nutshell, both participants featured deep convolutional neural network architectures (ResNet50 and EfficientNet). They completely avoided CNN ensembles and used geological locations in a test time. The Gokuleloop team approaches were focused on the domain specific fine-tuning where this team tried different pre-trained weights. With the Imagenet-21k weights, ResNet50 architecture, and naive probability weighting approach, Gokuleloop team achieved top F1 score of 0.625 while having a Log Loss of 0.83. The FHDO BCSG team approaches combined two stages. Firstly, they used a Mask R-CNN instance detection method for snake detection. Secondly, different EfficientNet models were used to classify regions detected by the previous stage. Their best submitted model was an EfficientNet-B4 fine-tuned from the ImageNet pre-trained checkpoint. This model achieves F1 score of 0.404 and a Log-Loss of 6.650. The high Log-Loss was achieved due to the application of softmax normalization after the multiplication of the location data which leads to small differences in the predictions. All submission and their achieved scores are reported in the Figure 12.

Conclusions and Perspectives

The main outcome of this collaborative evaluation is a new snapshot of the performance of state-of-the-art computer vision, bio-acoustic and machine learning techniques towards building real-world biodiversity monitoring systems. This study shows that recent deep learning techniques still allow some consistent progress for most of the evaluated tasks. The results of the PlantCLEF challenge, in particular, revealed that the last advances in domain adaptation enable the use of herbarium data to facilitate the identification of rare tropical species for which no or very few other training images are available. The results of the GeoLifeCLEF challenge were also highly relevant, revealing that deep convolutional neural networks trained on high-resolution geographic images are able to effectively predict species distribution even without using bioclimatic or soil variables. Furthermore, the results of the SnakeCLEF challenge showed that both traditional approaches and deep convolutional neural networks can benefit from geographical information.

Fig. 3 :

 3 Fig. 3: PlantCLEF 2020 results

Fig. 4 :

 4 Fig. 4: South American soundscapes often have an extremely high call density. The 2020 BirdCLEF test data contains 48 fully annotated soundscapes recorded in Peru.

Fig. 7 :

 7 Fig. 7: Occurrences distribution over the US and France. Blue dots represent training data, red dots represent test data.

Fig. 8 :

 8 Fig. 8: Adaptive top-30 accuracy and top-30 accuracy per run and participant on GeoLifeCLEF 2020 task.

Fig. 9 :

 9 Fig. 9: Medically important snake species (left) and similar-looking nonvenomous species (right). © Peter Vos, iNaturalist, CC-BY-NC and © Alex Rebelo, iNaturalist, CC-BY-NC and © Peter Vos, iNaturalist, CC-BY-NC and © Iris Melgar, iNaturalist, CC-BY-NC.

Fig. 10 :

 10 Fig. 10: Two observations of the same snake species (Boomslang, Dispholidus typus) with high visual dissimilarity related to sex (female left, male right). © Mark Heystek, iNaturalist, CC-BY-NC and © Daniel Rautenbach, iNaturalist, CC-BY-NC.

Fig. 11 :

 11 Fig. 11: Randomly selected images from the SnakeCLEF 2020 training set. © stewartb, iNaturalist, CC-BY-NC and © Jennifer Linde, iNaturalist, CC-BY-NC and © Gilberto Ponce Tejeda, iNaturalist, CC-BY-NC and © Ryan van Huyssteen, iNaturalist, CC-BY-NC and © Jessica Newbern, iNaturalist, CC-BY-NC.

F 1 = 2 ×

 2 Precision × Recall Precision + Recall This score represents the harmonic mean of the Precision and the Recall. The secondary metric was calculated as Multi-class Classification Logarithmic Loss e.g. Cross Entropy Loss. LogLoss = -M c=1 y o,c • log(p o,c )

Fig. 12 :

 12 Fig. 12: F1 Scores achieved within the SnakeCLEF 2020.

https://www.cbd.int/

http://www.lifeclef.org/

http://www.imageclef.org/

https://www.aicrowd.com

http://portal.idigbio.org/portal/search

https://www.xeno-canto.org/

National Agriculture Image Program, https://www.fsa.usda.gov

https://geoservices.ign.fr

http://osr-cesbio.ups-tlse.fr/ ~oso/posts/2017-03-30-carte-s2-2016/

https://lpdaac.usgs.gov/products/srtmgl1v003/

Most of the Stanford team's methods were based on deep neural networks, but the authors informed us that they encounter convergence issues resulting in performance poorer than expected.

Acknowledgements This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No°863463 (Cos4Cloud project), and the support of #DigitAG.


Bahria Khenfous-Djebari

Mohamed Kerkoud

Marion Fis- Cher-Le Saux

Traki Benhassine

Zouaoui Bouznad

Ralf Koebnik

Claude Bragard

Isolation of atypical wheat-associated xanthomonads in Algeria

Keywords: Xanthomonas, bacterial leaf streak, black chaff, wheat

Bacterial leaf streak and black chaff are important bacterial diseases of wheat, which have been reported to be caused by Xanthomonas translucens. In 2016, symptoms of bacterial leaf streak and black chaff were observed in Algeria, at experimental wheat breeding stations and in farmers' fields under sprinkler irrigation on two wheat cultivars, 'Hiddab' and 'Simeto' . Yellow Xanthomonas-like bacterial colonies were isolated from plant material, including leaves, spikes and post-harvest crop residues. Initial characterisation using biochemical, physiological and pathogenicity tests identified the bacteria as Xanthomonas. Diagnostic PCR targeting the 16S-23S rRNA intergenic region indicated that the strains were X. translucens, a clade-1 xanthomonad. However, partial DNA sequences of the housekeeping genes gyrB and rpoD revealed that the strains belong to clade 1, but likely represent a new Xanthomonas species that has not been previously described on wheat or other Gramineae. The most closely related strain, NCPPB 2654, was isolated from a bean plant in the United Kingdom in 1974. Further characterization is required to clarify the taxonomic status of the Algerian Xanthomonas isolates from wheat, and to determine their host ranges and impacts on plant cultivation.

INTRODUCTION

Wheat is a major crop worldwide, affected by some bacterial diseases, among which bacterial leaf streak (BLS) is the most important. BLS is caused by Xanthomonas translucens (ex Jones et al. 1917) [START_REF] Vauterin | The relations ships within the genus Xanthomonas and a proposal for a new classification[END_REF]. When symptoms occur on the wheat plant glumes, the disease caused by X. translucens is called black chaff (BC) [START_REF] Duveiller | The Bacterial Diseases of Wheat. Concepts and Methods of Disease Management[END_REF]. BLS is widely distributed in the world and the disease is prevalent in most regions where small-grain cereals are cultivated [START_REF] Paul | Bacterial pathogens of Gramineae: systematic review and assessment of quarantine status for the EPPO region[END_REF][START_REF] Duveiller | Effect of temperature and air humidity on multiplication of Xanthomonas campestris pv. undulosa and symptom expression in susceptible and field tolerant wheat genotypes[END_REF]. However, these diseases have not been extensively studied in North Africa, despite sporadic reports of occurrence in countries close to Algeria, including Libya [START_REF] Bragard | Genetic diversity among Xanthomonas campestris strains pathogenic for small grains[END_REF], Morocco and Tunisia (Sands and Fourest, 1989).

Yield losses caused by BLS are generally not considered problematic. However, losses of up to 40% have been recorded under conditions that are conducive for the pathogen [START_REF] Duveiller | The Bacterial Diseases of Wheat. Concepts and Methods of Disease Management[END_REF]. Algeria cultivates cereals on an area of 3.3 million ha, 1.3 million of which are irrigated and thus likely to be vulnerable to BLS. Furthermore, more than 20% of yield may be lost if 50% of flag leaf area is affected by the disease [START_REF] Duveiller | Study on yield loss due to Xanthomonas campestris pv. undulosa in wheat under high rainfall temperature condition[END_REF]. BLS generally appears late in the growing season in regions with temperate climate or in warmer environments characterized by cool nights and frequent temperature variations [START_REF] Duveiller | Bacterial leaf streak and black chaff[END_REF]. The symptoms are usually more obvious after heading [START_REF] Wiese | Compendium of Wheat Diseases[END_REF]. All aerial parts of host plants can be affected, but the leaves and glumes are more often affected than the other parts. In cases of severe damage, the seeds can be blackened and wrinkled [START_REF] Zillinsky | Common Diseases of Small Grain Cereals. A Guide to Identification[END_REF]. BC is characterized by many black longitudinal stripes on the upper portions of the glumes [START_REF] Smith | A new disease of wheat[END_REF], that can be identified by greasy appearance. Yellow bacterial droplets exude along the lesions, particularly in wet weather.

Xanthomonas species are known for their ability to adhere to and colonize host leaf surfaces as epiphytes before invading the intercellular spaces [START_REF] Boulanger | The plant pathogen Xanthomonas campestris pv. campestris exploits N-acetylglucosamine during infection[END_REF][START_REF] Dutta | Interactions of seedborne bacterial pathogens with host and non-host plants in relation to seed infestation and seedling transmission[END_REF][START_REF] Zarei | Epiphytic growth of Xanthomonas arboricola and Xanthomonas citri on nonhost plants[END_REF]. Xanthomonads have evolved several strategies for successful infection, including mechanisms to suppress host plant resistance and access nutrients from host cells [START_REF] Büttner | Regulation and secretion of Xanthomonas virulence factors[END_REF][START_REF] Senthil-Kumar | Plant and pathogen nutrient acquisition strategies[END_REF][START_REF] Jacques | Using ecology, physiology, and genomics to understand host specificity in Xanthomonas[END_REF]. However, much less is known for X. translucens, which belongs to xanthomonad clade 1, while most functional research has been carried out with clade-2 xanthomonads [START_REF] Parkinson | Phylogenetic analysis of Xanthomonas species by comparison of partial gyrase B gene sequences[END_REF]. The importance of the bacterial type III secretion system and TAL effectors for pathogenicity has been demonstrated [START_REF] Wichmann | The noncanonical type III secretion system of Xanthomonas translucens pv. graminis is essential for forage grass infection[END_REF][START_REF] Peng | Long read and single molecule DNA sequencing simplifies genome assembly and TAL effector gene analysis of Xanthomonas translucens[END_REF][START_REF] Charkhabi | Complete genome sequencing and targeted mutagenesis reveal virulence contributions of Tal2 and Tal4b of Xanthomonas translucens pv. undulosa ICMP11055 in bacterial leaf streak of wheat[END_REF][START_REF] Pesce | Comparative genomics identifies a novel conserved protein, HpaT, in proteobacterial type III secretion systems that do not possess the putative translocon protein HrpF[END_REF].

Since no data are available on bacterial diseases of small grain cereals in Algeria, the objective of this study was to assess the presence of wheat-associated xanthomonads in this country, to verify their ability to cause BLS on cereals and to determine their identity. This research was based on morphological, biochemical and physiological characterization of bacterial isolates, complemented by pathogenicity tests on host plants and DNA-based molecular diagnostics.

MATERIALS AND METHODS

Bacterial strains

Bacteria were isolated from symptomatic wheat leaf and spike samples and from post-harvest plant residues originating from fields that had shown symptoms of BLS and BC in the previous growing season (Table 1) (Kar- avina et al., 2008). Samples (10 g each) of plant organs or post-harvest stubble residues were each ground to a fine powder and mixed with 50 mL phosphate-buffered saline (PBS). The resulting cell suspension was shaken for 20 min and allowed to settle for 3 h. Series of tenfold dilutions were prepared from the suspension supernatants and appropriate amounts of each dilution were plated on standard nutrient agar medium and on semiselective Wilbrink's medium supplemented with 0.75 g L -1 of boric acid, 10 mg L -1 of cephalexin and 75 mg L -1 of cycloheximide (WBC medium) to reduce fungal growth [START_REF] Duveiller | A seed detection method of Xanthomonas campestris pv. undulosa, using a modification of Wilbrink's agar medium[END_REF]. For comparison, X. translucens pv. undulosa strain UPB753, which had been isolated from wheat in Brazil [START_REF] Bragard | Genetic diversity among Xanthomonas campestris strains pathogenic for small grains[END_REF], was used as a reference strain. Pure cultures were obtained upon cultivation at 30°C. Based on morphological characteristics, Xanthomonas-like bacterial strains were assigned a designation number and kept at 4°C on glucose, yeast extract-calcium carbonate agar (GYCA) tubes for shortterm conservation and at -80°C in 20% glycerol for longterm storage.

Phenotypic characterization

Established tests were used to identify the bacteria [START_REF] Bradbury | Guide to Plant Pathogenic Bacteria[END_REF][START_REF] Van Den Mooter | Numerical analysis of 295 phenotypic features of 266 Xanthomonas strains and related strains and an improved taxonomy of the genus[END_REF][START_REF] Schaad | Laboratory Guide for Identification of Plant Pathogenic Bacteria, Third Edition[END_REF]. These included formation of mucoid colonies on GYCA medium, Gram reaction using the KOH test, oxidase test using tetramethyl-p-phenylenediamine dihydrochloride reagent, oxidative and fermentative metabolism of glucose, hydrolysis of Tween 80, aesculin and starch, production of levane sucrase, production of catalase, liquefaction of gelatine, H 2 S production from cysteine, nitrate reduction, growth at 35°C, and growth on 2% and 5% NaCl media.

DNA manipulations

For rapid tests, bacterial cells were lysed by brief boiling and then directly used for PCR, as described previously [START_REF] Maes | Recognition and detection in seed of the Xanthomonas pathogens that cause cereal leaf streak using rDNA spacer sequences and polymerase chain reaction[END_REF]. For PCR amplification of housekeeping genes, DNA was isolated using the Wizard ® Genomic DNA Purification Kit (Promega Corp.), following the manufacturer's instructions.

PCR amplification of the alanine-specific tRNA gene in the 16S-23S rRNA intergenic region was performed as described previously [START_REF] Maes | Recognition and detection in seed of the Xanthomonas pathogens that cause cereal leaf streak using rDNA spacer sequences and polymerase chain reaction[END_REF], with modifications. The reaction mixture was prepared in a total volume of 25 μL comprising 5 μL of 5 × PCR buffer, 2.5 μL MgCl 2 (25 mM), 0.75 μL dNTP mixture (25 mM), 0.5 μL of each PCR primer at 10 μM (T1, 5'-CCGC-CATAGGGCGGAGCACCCCGAT; T2, 5'-GCAGGT-GCGACGTTTGCAGAGGGATCTGCAAATC), 2.5 μL DNA sample (50 ng μL -1 ), 0.2 μL Taq polymerase (Promega), and 13.05 μL distilled water. PCR was performed with the following conditions: 90°C for 2 min, 29 cycles of 93°C for 30 s, 50°C for 30 s, 72°C for 30 s, and a final extension for 10 min at 72°C. The PCR products were separated by electrophoresis on 2% agarose gel in TAE buffer, stained with Midori green (Nippon Genetics Europe) and visualized under UV light.

Previously published MLSA primers were used for PCR amplification and partial DNA sequencing of two housekeeping genes, gyrB and rpoD [START_REF] Fargier | Pathogenicity assays restrict the species Xanthomonas campestris into three pathovars and reveal nine races within X. campestris pv. campestris[END_REF]. PCR amplifications were performed as recommended [START_REF] Mhedbi-Hajri | Evolutionary history of the plant pathogenic bacterium Xanthomonas axonopodis[END_REF] in a 50 μL reaction mixture containing 1 × GoTaq ® buffer, 200 μM dNTP, 0.5 μM of each primer, 0.4 U of GoTaq ® DNA polymerase (Promega), and 3 ng of genomic DNA, with an initial denaturation at 94°C for 2 min, 30 cycles of denaturation for 1 min at 94°C, annealing for 1.5 min at 60°C, extension for 1.5 min at 72°C, and a final extension for 10 min at 72°C. 8 μL of PCR products reaction mixtures were analysed by electrophoresis on 1.5% agarose gel in TAE buffer, stained with Midori green direct and visualized under UV light. The remaining amplified PCR products were purified with the Wizard ® PCR clean-up kit (Promega) and sequenced with reverse and forward primers using BigDye Terminator v3.1 cycle sequencing kit (Applied Biosystems). Both forward and reverse sequences were aligned and manually edited before deposition in the GenBank database (Table 1).

Pathogenicity tests

Bacterial cells were suspended in sterile solution of 0.90% (w/v) of NaCl and the concentration of cells was adjusted to 1 × 10 9 CFU mL -1 for hypersensitive reaction tests on tobacco plants of the variety Xanthi and to 1 × 10 7 CFU mL -1 for pathogenicity tests. Sterile saline solution served as negative controls in the pathogenicity assays.

All strains were tested for pathogenicity, by inoculation on the sensitive wheat cultivar 'Acsad 885', using three different assays. First, after injection of sterile water into plant leaf sheath at 2.5 cm above soil level, three-leaf stage seedlings were puncture inoculated with a sterile needle that had been passed through a bacterial colony ("pricking inoculation") [START_REF] Bragard | Pathogenic variation in Xanthomonas campestris pv. undulosa[END_REF]. Second, using a needle-less plastic syringe, bacterial suspensions were infiltrated through the upper leaf surfaces until appearance of liquid-soaked areas of about 2 cm length ("leaf infiltration") [START_REF] Bragard | Pathogenic variation in Xanthomonas campestris pv. undulosa[END_REF]. Third, whole leaves were immersed into bacterial solutions for 20 sec ("dip inoculation") [START_REF] Darsonval | Adhesion and fitness in the bean phyllosphere and transmission to seed of Xanthomonas fuscans subsp. fuscans[END_REF]. Plants were incubated at 28°C and 95% relative humidity with a photoperiod of 16h/8h (day/night), and symptoms were scored over time.

To re-isolate bacteria from infected plant material, symptomatic leaf segments were cut into small pieces in sterile physiological saline and plated on standard and semi-selective media.

Bioinformatic analyses

To link the different strains with their respective taxa among the species of Xanthomonas, corresponding gyrB and rpoD gene portions were retrieved from Gen-Bank and PAMDB databases (https://www.ncbi.nlm.nih. gov, http://www.pamdb.org) [START_REF] Almeida | PAMDB, a multilocus sequence typing and analysis database and website for plantassociated microbes[END_REF][START_REF] Sayers | Database resources of the National Center for Biotechnology Information[END_REF]. For recently described species and pathovars that are not represented in PAMDB, such as "Xanthomonas pseudalbilineans", X. maliensis, X. floridensis, X. nasturtii, and X. prunicola, corresponding sequences were extracted from the genome sequences (Supplementary Table 1) [START_REF] Pieretti | Full genome sequence analysis of two isolates reveals a novel Xanthomonas species close to the sugarcane pathogen Xanthomonas albilineans[END_REF][START_REF] Triplett | Characterization of a novel clade of Xanthomonas isolated from rice leaves in Mali and proposal of Xanthomonas maliensis sp[END_REF]Hersemann et al., 2016b;[START_REF] Vicente | Pathogenic, phenotypic and molecular characterisation of Xanthomonas nasturtii sp. nov. and Xanthomonas floridensis sp. nov., new species of Xanthomonas associated with watercress production in Florida[END_REF][START_REF] López | Xanthomonas prunicola sp. nov., a novel pathogen that affects nectarine (Prunus persica var. nectarina) trees[END_REF].

Multiple sequence alignments were performed using the MUSCLE algorithm (https://www.ebi.ac.uk/Tools/ msa/muscle/) [START_REF] Edgar | MUSCLE: multiple sequence alignment with high accuracy and high throughput[END_REF]. Phylogenetic trees were generated using the phylogeny.fr pipeline, with default parameters (http://www.phylogeny.fr) [START_REF] Dereeper | Phylogeny.fr: robust phylogenetic analysis for the non-specialist[END_REF]. Newick files were generated and the tree was manipulated using the iTOL website (https://itol.embl. de) [START_REF] Letunic | Interactive Tree Of Life v2: online annotation and display of phylogenetic trees made easy[END_REF] to improve visualization.

RESULTS

Isolation of bacteria from wheat

BLS symptoms were observed in various plots of the Algiers experimental station, at the tillering and at the heading crop growth stages (Figure 1A). Additionally, severe disease symptoms of BC were observed at the heading stage (Figure 1B). Affected varieties in the Algiers area included wheat 'Hiddab' (HD1220), and also several breeding lines and cultivars grown at the Algiers experimental station for studies under the pedoclimatic conditions of the region, to verify their performance, efficiency, specific features and disease resistance. Symptoms were also observed on the cultivar 'Simeto', grown under the sprinkler irrigation at El Ménéa (El Goléa), South Algeria. This is an area characterized by cool nights and high day temperatures. Furthermore, dur-ing the 2016 agricultural campaign, the disease was sporadically present in plots of the Algiers experimental station, and more widespread in plots under pivot irrigation, where 'Simeto' was sown. Yellow colonies on media, resembling Xanthomonas, were easily isolated from the plant symptoms. In order to evaluate if post-harvest material could serve as reservoirs for infections, crop residues from plots at the Algiers multiplication station that had shown symptoms, were analysed as well, as described previously [START_REF] Karavina | The contribution of soil and crop debris inocula to the outbreak of bacterial common blight in field beans (Phaseolus vulgaris L) under Zimbabwean conditions[END_REF]. Xanthomonas-like bacteria were also isolated from this material.

Phenotypical characterization of bacteria isolated from wheat

Among all the strains obtained from the different origins, 30 were retained (Table 2) with consistent biochemical and physiological test responses corresponding to those obtained with the X. translucens reference strain [START_REF] Bradbury | Guide to Plant Pathogenic Bacteria[END_REF]; Van den Mooter and Swings, 1990; [START_REF] Schaad | Laboratory Guide for Identification of Plant Pathogenic Bacteria, Third Edition[END_REF]. All these strains grew as mucoid and yellow pigmented colonies, and they were negative for Gram staining, oxidase activity and nitrate reduction. The strains could hydrolyse aesculin, gelatine and starch and produced catalase, levane sucrase, lipase and hydrogen sulphide from cysteine. Bacteria grew at 35°C and in nutrient broth supplemented with 2% sodium chloride, but not when supplemented with 5% sodium chloride. All strains triggered hypersensitive reactions on tobacco. These analyses indicated that the wheat-associated bacteria belonged to the genus Xanthomonas and may be related to X. translucens.

Pathogenicity assays with xanthomonads isolated from wheat

Three inoculations methods were applied to evaluate the pathogenicity of the bacterial strains. Upon leaf infiltration of a susceptible cultivar, chlorotic to necrotic lesions developed within 7 d after infection (Figure 1C). When pricking three-leaf stage wheat seedlings, similar symptoms were observed 8 d after inoculation (Figure 1D). Dip inoculation of wheat leaves resulted in symptoms that were clearly visible after 8 d, including typical water-soaked spots associated with bacterial exudates from the plant organs (Figure 1E). Bacteria were re-isolated from infected plant material. Morphological, biochemical and physiological characterization confirmed the identity of the re-isolated bacteria with the inoculum, thus fulfilling the Koch's postulates.

DNA-based diagnostics of xanthomonads isolated from wheat

In order to evaluate whether the strains belong to X. translucens, they were subjected to a protocol that had been developed for specific detection of this species, based on a discriminatory region in the 16S-23S intergenic region, which encodes two tRNAs [START_REF] Maes | Recognition and detection in seed of the Xanthomonas pathogens that cause cereal leaf streak using rDNA spacer sequences and polymerase chain reaction[END_REF]. A DNA fragment with a size of 139 bp was amplified with PCR primers T1 and T2 for all 30 strains.

To further characterize ten representative strains from wheat, a portion of the gyrB gene that was previously used in multiple locus sequence analysis (MLSA) was amplified by PCR and sequenced, using previously developed primers [START_REF] Fargier | Pathogenicity assays restrict the species Xanthomonas campestris into three pathovars and reveal nine races within X. campestris pv. campestris[END_REF][START_REF] Young | A multilocus sequence analysis of the genus Xanthomonas[END_REF]. All sequences were identical. Homologous sequences of type, pathotype or other Xanthomonas strains were retrieved from the PAMDB database [START_REF] Almeida | PAMDB, a multilocus sequence typing and analysis database and website for plantassociated microbes[END_REF]. In addition, sequences for those of Xanthomonas species that were not available at PAMDB, but had been included in a previous gyrB-based phylogenetic study, including sequences for undescribed species ("slc" species-level clades) [START_REF] Parkinson | Phylogenetic structure of Xanthomonas determined by comparison of gyrB sequences[END_REF], were used for comparison. Sequences were aligned using MUSCLE and manually trimmed to 528 bp. A phylogenetic tree was calculated using the Phylogeny.fr pipeline (Figure 2). This analysis revealed that the Algerian sequences clustered with other sequences from clade-1 xanthomonads, including Xanthomonas hyacinthi, X. theicola and X. translucens. The closest sequence corresponded to strain NCPPB 2654 from species-level clade 5. This strain was isolated in 1974 by F. W. Catton, from navy bean (Phaseolus vulgaris) in the United Kingdom. No other sequence information is available for this species-level clade.

This result prompted us to partially sequence another housekeeping gene rpoD, that was previously used in MLSA studies [START_REF] Young | A multilocus sequence analysis of the genus Xanthomonas[END_REF]. Multiple sequence alignment of four 870-bp sequences from representative Algerian strains revealed their identity with each other. A phylogenetic tree was generated including representative haplotypes for clade-1 xanthomonads from PAMDB. In addition, sequences from three additional X. translucens pathotype strains and two sequences belonging to the recently suggested clade-1 species "X. pseudalbilineans" were included [START_REF] Pieretti | Full genome sequence analysis of two isolates reveals a novel Xanthomonas species close to the sugarcane pathogen Xanthomonas albilineans[END_REF]Hersemann Table 2. Biochemical and physiological tests used to identify bacterial isolates from wheat, and a reference strain (Xanthomonas translucens pv. undulosa strain UPB753 [START_REF] Bragard | Genetic diversity among Xanthomonas campestris strains pathogenic for small grains[END_REF] [START_REF] Maes | Recognition and detection in seed of the Xanthomonas pathogens that cause cereal leaf streak using rDNA spacer sequences and polymerase chain reaction[END_REF] + + et al., 2016b). This analysis confirmed that the Algerian strains belong to clade-1, but did not cluster with any of the six described species. This indicates that the Algeria strains from wheat belong to another species, with strain NCPPB 2654 as the likely founder (Figure 3).

DISCUSSION

Diseased wheat plants were reported from several plots in Algeria, with symptoms on the leaves and spikes as well as melanotic areas on the glumes, that were similar to those described for leaf streak and black chaff [START_REF] Duveiller | Bacterial leaf streak and black chaff[END_REF]. These diseases result from bacterial infections, often in high temperature and high humidity conditions, and the observed symptoms have long been described for these diseases [START_REF] Smith | A new disease of wheat[END_REF][START_REF] Johnson | Melanism in wheat induced by high temperature and humidity[END_REF]. The strains characterized in the present study were mostly obtained from sprinkler-irrigated fields or from breeding stations where genotype behaviour was being assessed.

All strains obtained from affected wheat samples, including leaves, spikes and crop residues, had phenotypic characteristics that corresponded to those described in the literature for X. translucens. Moreover, inoculation of wheat seedlings at the three-leaf stage caused water-soaked lesions within 8 d after inoculation, accompanied by signs of necrosis around the inoculat- Representative strains of all species following taxonomic revisions of Xanthomonas gardneri and X. axonopodis species complex are included [START_REF] Constantin | Genetic characterization of strains named as Xanthomonas axonopodis pv. dieffenbachiae leads to a taxonomic revision of the X. axonopodis species complex[END_REF][START_REF] Timilsina | Reclassification of Xanthomonas gardneri (ex Šutič 1957) Jones et al. 2006 as a later heterotypic synonym of Xanthomonas cynarae Trébaol et al. 2000 and description of X. cynarae pv. cynarae and X. cynarae pv. gardneri based on whole genome analyses[END_REF]. Taxonomically unassigned species-level clades (Slc 1-7) are indicated [START_REF] Parkinson | Phylogenetic structure of Xanthomonas determined by comparison of gyrB sequences[END_REF]. All sequences were trimmed to the portion that is available in GenBank for the Xanthomonas phaseoli type strain (528 bp, Accession number KT585789). The tree was constructed with the Phylogeny.fr pipeline, using default parameters, and graphically edited using the iTOL suite. All nodes were supported by bootstrap values greater than 0.75, except for those marked with a stop symbol. The scale of branch lengths is indicated at the top left.

ed areas and ultimately causing the death of the leaves. When the pricking inoculation method was used, initial local necrosis expanded with time and affected whole leaf blades, concomitantly showing typical exudate droplets. The inoculation techniques mimicked temperature and moisture conditions conducive for the disease [START_REF] Duveiller | Study on yield loss due to Xanthomonas campestris pv. undulosa in wheat under high rainfall temperature condition[END_REF][START_REF] Duveiller | The Bacterial Diseases of Wheat. Concepts and Methods of Disease Management[END_REF]. These results confirmed that the Algerian Xanthomonaslike strains were pathogenic on wheat cultivar 'Acsad 885'. Bacteria could also be isolated from crop residues 3 to 4 weeks after harvest, indicating that the pathogen can survive on plant material. This may serve as reservoirs for new infections in the next cropping cycle. Similar observations have been made for X. translucens, which was found to survive on crop debris for more than 30 months under laboratory conditions, and for less than 8 months under field conditions [START_REF] Malavolta | Identification and survival of Xanthomonas translucens pv. cerealis in seeds and crop debris of wheat[END_REF]. Occurrence on, and isolation from, wheat plants and the symptoms observed in the fields and upon artificial inoculation strongly indicated that the strains were X. translucens.

Initial molecular characterization of the strains using a PCR assay that was developed for detection of X. translucens, including pathovars infecting smallgrain cereals (pvs. cerealis, hordei, secalis, translucens and undulosa) and those infecting forage grasses (pvs. arrhenatheri, graminis, phlei, phleipratensis and poae), further supported that the Algerian strains were X. translucens [START_REF] Maes | Recognition and detection in seed of the Xanthomonas pathogens that cause cereal leaf streak using rDNA spacer sequences and polymerase chain reaction[END_REF]. This assay targets the 16S-23S intergenic region, which encodes two tRNAs in all xanthomonads, one for alanine (UGC anticodon) and one for isoleucine (GAU anticodon). The diagnostic primers T1 and T2 anneal immediately upstream and downstream of the tRNA (Ala) gene. Most xanthomonads have short regions of 14 to 19 bp between the transcribed sequences for the tRNA (Ala) and the tRNA (Ile) [START_REF] Gonçalves | Phylogenetic analysis of Xanthomonas species based upon 16S-23S rDNA intergenic spacer sequences[END_REF], and therefore lack the target region for the T2 primer. However, X. translucens, two other clade-1 species (X. hyacinthi, X. theicola) and two clade-2 species (Xanthomonas codiaei, Xanthomonas melonis) have longer regions of 75 to 79 bp, that are fairly conserved and might allow annealing of the T2 primer under less stringent conditions (data not shown). Since the region corresponding to the T1 primer is less similar for X. codiaei and X. melonis, the PCR should not amplify the diagnostic DNA fragment of 139 bp, as had been confirmed for X. melonis [START_REF] Maes | Recognition and detection in seed of the Xanthomonas pathogens that cause cereal leaf streak using rDNA spacer sequences and polymerase chain reaction[END_REF]. However, that the PCR could amplify the diagnostic DNA fragment for bacteria of the X. hyacinthi-X. theicola-X. translucens subclade cannot be excluded. When the assay was developed by Maes and co-workers, all xanthomonads that were known as pathogens on Gramineae (i.e. X. albilineans, X. axonopodis, X. bromi, X. oryzae and X. vasicola), and representative strains of most described species of Xanthomonas, were included, although some species of clade-1 were not tested (e.g. X. hyacinthi and X.theicola). Yellow disease of hyacinth, a monocot of the Asparagaceae, was the first disease described to be caused by Xanthomonas [START_REF] Van Doorn | Xanthomonas campestris pv. hyacinthi: cause of yellow disease in Hyacinthus[END_REF]. Infection of asparagus by X. translucens has been reported [START_REF] Rademaker | Classification and identification of Xanthomonas translucens isolates, including those pathogenic to ornamental asparagus[END_REF]. Therefore, the taxonomic status of the Algerian strains remained uncertain based on the diagnostic PCR.

Since we felt that the diagnostic PCR is not able to unambiguously identify strains of X.translucens, two housekeeping genes that are included in MLSA schemes were analysed [START_REF] Young | A multilocus sequence analysis of the genus Xanthomonas[END_REF]. Partial sequences of both genes, gyrB and rpoD, clustered with sequences from other clade-1 xanthomonads, such as X. hyacinthi, X. theicola and X. translucens, but were distant enough to question whether they belonged to any of the described species. The gyrB gene has been used for exhaustive phylogenetic analyses of Xanthomonas, including strains from species-level clades that still await precise taxonomic assignment [START_REF] Parkinson | Phylogenetic analysis of Xanthomonas species by comparison of partial gyrase B gene sequences[END_REF][START_REF] Parkinson | Phylogenetic structure of Xanthomonas determined by comparison of gyrB sequences[END_REF]. The partial gyrB gene sequences from the Algerian isolates were very similar to that of strain NCPPB 2654, which was isolated from a navy bean plant in the United Kingdom (https://www.fera.co.uk/ncppb). According to the NCPPB website, this strain has a fatty acid profile typical of Xanthomonas, but is not pathogenic on bean pods. It would be interesting to know wheth- Sequences were trimmed to the size of the sequences that were retrieved from PAMDB (855 bp for X. translucens and the Algerian strain). The phylogenetic tree was constructed with the Phylogeny.fr pipeline, using default parameters, and graphically edited using the iTOL suite. All nodes were supported by bootstrap values greater than 0.75, except for those marked with a stop symbol. The scale of branch lengths is indicated at the top left. er this strain was isolated near a wheat field, and to test this strain for pathogenicity on wheat plants. Likewise, the next similar sequence corresponded to strain NCP-PB 2983, which was deposited as Xanthomonas campestris pv. phormiicola and belongs to species-level clade 6. This strain was isolated in Japan from New Zealand flax (Phormium tenax), a member of the Asparagales (Asphodelaceae). Three species related to the Algerian strains, X. hyacinthi, X. translucens and X. campestris pv. phormiicola, are able to colonize plants in the Asparagales, and future work will evaluate whether the Algerian strains from wheat can infect these plants as well.

In conclusion, this is the first description of wheatpathogenic xanthomonads from Algeria, which were atypical in that they most likely do not belong to X. translucens. Further characterization, ideally including whole-genome sequencing, will clarify their taxonomic status and their host range [START_REF] Peng | Long read and single molecule DNA sequencing simplifies genome assembly and TAL effector gene analysis of Xanthomonas translucens[END_REF][START_REF] Langlois | Characterization of the Xanthomonas translucens complex using draft genomes, comparative genomics, phylogenetic analysis, and diagnostic LAMP assays[END_REF]. It will also be important to compare these strains with other bacterial pathogens of cereals, and to elucidate whether candidate type III effectors, phytohormones and/or toxins are involved in pathogenicity and host adaptation [START_REF] Royer | Genome mining reveals the genus Xanthomonas to be a promising reservoir for new bioactive non-ribosomally synthesized peptides[END_REF][START_REF] Gardiner | Genomic analysis of Xanthomonas translucens pathogenic on wheat and barley reveals cross-kingdom gene transfer events and diverse protein delivery systems[END_REF]Hersemann et al., 2016aHersemann et al., , 2016b[START_REF] Hersemann | Comparative genomics of host adaptive traits in Xanthomonas translucens pv. graminis[END_REF][START_REF] Triplett | AvrRxo1 is a bifunctional type III secreted effector and toxin-antitoxin system component with homologs in diverse environmental contexts[END_REF][START_REF] Nagel | Investigating the phylogenetic range of gibberellin biosynthesis in bacteria[END_REF].

Figure 1 .

 1 Figure 1. Disease symptoms on wheat. (A) Symptoms of bacterial leaf streak at the heading stage, (B) symptoms of black chaff at the heading stage, (C) chlorotic to necrotic lesions from leaf infiltration 7 d after inoculation, (D) disease symptoms 8 d after pricking inoculation of wheat seedlings at the three-leaf stage, and (E) watersoaked spots associated with bacterial exudates 8 d after dip inoculation of leaves.

Figure 2 .

 2 Figure 2. gyrB-based phylogenetic classification of the Algerian wheat-associated xanthomonads.Representative strains of all species following taxonomic revisions of Xanthomonas gardneri and X. axonopodis species complex are included[START_REF] Constantin | Genetic characterization of strains named as Xanthomonas axonopodis pv. dieffenbachiae leads to a taxonomic revision of the X. axonopodis species complex[END_REF][START_REF] Timilsina | Reclassification of Xanthomonas gardneri (ex Šutič 1957) Jones et al. 2006 as a later heterotypic synonym of Xanthomonas cynarae Trébaol et al. 2000 and description of X. cynarae pv. cynarae and X. cynarae pv. gardneri based on whole genome analyses[END_REF]. Taxonomically unassigned species-level clades (Slc 1-7) are indicated[START_REF] Parkinson | Phylogenetic structure of Xanthomonas determined by comparison of gyrB sequences[END_REF]. All sequences were trimmed to the portion that is available in GenBank for the Xanthomonas phaseoli type strain (528 bp, Accession number KT585789). The tree was constructed with the Phylogeny.fr pipeline, using default parameters, and graphically edited using the iTOL suite. All nodes were supported by bootstrap values greater than 0.75, except for those marked with a stop symbol. The scale of branch lengths is indicated at the top left.

Figure 3 .

 3 Figure3. rpoD-based phylogenetic classification of the Algerian wheat-associated xanthomonads. Sequences were trimmed to the size of the sequences that were retrieved from PAMDB (855 bp for X. translucens and the Algerian strain). The phylogenetic tree was constructed with the Phylogeny.fr pipeline, using default parameters, and graphically edited using the iTOL suite. All nodes were supported by bootstrap values greater than 0.75, except for those marked with a stop symbol. The scale of branch lengths is indicated at the top left.

Table 1 .

 1 Details of Algerian bacterial isolates obtained from wheat.

	Isolate Gene	GenBank Accession number	Sample	Symptoms a	Wheat cultivar	Location	Year
	X1	gyrB rpoD	MF142045 MF142046	Leaf	BLS	'Simeto'	El Goléa	2016
	X2	gyrB	MF142047	Leaf	BLS	'Simeto'	El Goléa	2016
	X3	gyrB	MF142048	Leaf	BLS	'Simeto'	El Goléa	2016
	X4	gyrB	MF142049	Leaf	BLS	'Simeto'	El Goléa	2016
	X5	gyrB	MF142050	Crop residue	No visible symptoms 'Hiddab' (HD1220) Algiers experimental station	2016
	X8	gyrB rpoD	MF142051 MF142052	Spike	BC	'Simeto'	El Goléa	2016
	X12	gyrB rpoD	MF142053 MF142054	Crop residue	No visible symptoms 'Hiddab' (HD1220) Algiers experimental station	2010
	X13	gyrB rpoD	MF142055 MF142056	Crop residue	No visible symptoms 'Hiddab' (HD1220) Algiers experimental station	2010
	X16	gyrB	MF142057	Spike	BC	Breeding line	Algiers experimental station	2016
	X17	gyrB	MF142058	Spike	BC	Breeding line	Algiers experimental station	2016

a BLS = bacterial leaf streak, BC = black chaff.

  ).

	Test	Algerian isolates	Reference strain
	Mucoid and yellow colonies on GYCA medium	+	+
	Gram staining	-	-
	Oxidase	-	-
	Metabolism of glucose	oxidative oxidative
	Tween 80 hydrolysis	+	+
	Aesculin hydrolysis	+	+
	Starch hydrolysis	+	+
	Levane sucrase	+	+
	Catalase	+	+
	Liquefaction of gelatine	+	+
	H 2 S production from cysteine	+	+
	Nitrate reduction to nitrite	-	-
	Growth at 35 °C	+	+
	Growth in 2% NaCl	+	+
	Growth in 5% NaCl	-	-
	Hypersensitive reaction on tobacco	+	+
	Pathogenicity on wheat cv. Acsad 885	+	+
	Diagnostic PCR

ACKNOWLEDGEMENTS

Part of this research was carried out in the laboratory of the Earth and Life Institute at UC-Louvain. The authors thank the team in this laboratory, with special thanks to Pr H. Maraite and to Mrs L.N.Salhi. Mr Y.A.Merdoukh's assistance with field sampling is gratefully acknowledged.


Giulia Marchello
email: <giulia.marchello@inria.fr>.

Marco Corneli

Charles Bouveyron

The Dynamic Latent Block Model for Sparse and Evolving Count Matrices

HAL is

Introduction

In many applications, it is now frequent to have to summarize large matrices with a large amount of missing data that may evolve along the time. For instance, such data are commonly produced by e-commerce systems which record in continuous time all purchases of products made by customers. It is of great interest for those companies to cluster both customers and products to better understand the purchasing behaviors for marketing and purchase prediction. The simultaneous clustering of rows and columns of matrices is known as a co-clustering problem. We propose in this paper to add a third dimension of analysis to co-clustering by handling the dynamic of the count data generation.

The latent block model (LBM) is often used as a basis for many model-based methods for co-clustering. This model was proposed for the first time by [START_REF] Govaert | Clustering with block mixture models[END_REF] and it is based on the assumption that rows and columns are grouped in hidden clusters. In the last decade, the model has been extended allowing to deal with counting data [START_REF] Nadif | Model-based co-clustering for continuous data[END_REF], real data [START_REF] Lomet | An approximation of the integrated classification likelihood for the latent block model[END_REF], categorical data [START_REF] Keribin | Estimation and selection for the latent block model on categorical data[END_REF], ordinal data [START_REF] Jacques | Model-based co-clustering for ordinal data[END_REF][START_REF] Corneli | Co-clustering of ordinal data via latent continuous random variables and not missing at random entries[END_REF] and functional data [START_REF] Bouveyron | The functional latent block model for the co-clustering of electricity consumption curves[END_REF].

In this work, we extend the latent block model to the dynamic case by relying on a non-homogeneous Poisson process, with a latent partition of time intervals, for modeling the temporal data generation process. Such an approach has been already used, in a different context and with a different inference, by [START_REF] Corneli | Multiple change points detection and clustering in dynamic networks[END_REF] for clustering dynamic networks. We propose here a SEM-Gibbs algorithm for model inference and to make use of the ICL criterion for model selection. The proposed model, named dynamic latent block model (dLBM), allows therefore to discover latent partitions for rows and columns, but also for the time periods. Thus, dLBM provides a meaningful summary of a massive set of data, even with a large number of missing data. We present experiments on data set extracted from Amazon to illustrate the main features of our approach.

The dynamic latent block model

In this section, we introduce the dynamic latent block model (dLBM), the main goal of this model is the simultaneous clustering of rows and columns of high-dimensional sparse matrices in a dynamic time framework. The data we consider are organized such that we denoted as i = 1, ..., N the index of individuals (rows) and as j = 1, ..., P the index of objects (columns). We also consider a time period [0,T] during which the total number of rows, N , and columns, P , is fixed. Moreover, we indicate as X ij (t) the matrix that contains the number of interactions occurring between the individual i and the item j at time t ∈ [0, T ]. When no interaction between individuals and objects occurs, we have therefore missing values and the number of interactions is 0 for time t. Following [START_REF] Corneli | Block modelling in dynamic networks with non-homogeneous poisson processes and exact icl[END_REF], we further assume that the number of interactions between individuals and objects follows a non-homogeneous Poisson process (NHPP) where the intensity function λ(t) only depends on the clusters they belong to. The latent structure of rows and columns of the matrix X(t) is identified by:

• z = (z ik ; i = 1, ..., N ; k = 1, ..., K) : represents the clustering of rows into K groups: A 1 , ..., A K . Row i belongs to cluster A k iff z ik = 1 and z i = (z ik ) k ∈ {0 , 1 } K is the group indicator of row i;

• w = (w j ; j = 1, ..., P ; = 1, ..., L): represents the clustering of columns into L groups: B 1 , ..., B L .

Column j belongs to cluster B iff w j = 1 and w j = (w j ) ∈ {0 , 1 } L is the group indicator of column j;

Moreover, z and w are assumed to be independent and that they are distributed as follows:

p(z|γ) = K k=1 γ |A k | k , ( 1
)
where

γ k = P{z i = k}; K k=1 γ k = 1 and |A k | represents the number of rows in the cluster A k . p(w|ρ) = L =1 ρ |B | , (2)
where ρ = P{w j = };

L =1 ρ = 1 and |B | represent
the number of columns in the cluster B . As mentioned previously, a non-homogeneous Poisson process (NHPP) is used to count the interactions between the row i and the column j up to time t ∈ [0, T ], denoted by X ij (t):

X ij (t)|z ik w j = 1 ∼ P t 0 λ k (u)du , (3)
where λ k (t) represents the intensity function that only depends on the considered row cluster k and on the column cluster . Moreover, λ k (t) has to be positive and integrable on the time interval [0, T ].

In order to ease the understanding of the time dimension, we also assume that the whole continuous time period can be split in time clusters on which the data generation process is stable. It is worth noticing that a specific time cluster can occur more than once in the temporal line when its peculiar features are repeated after some time. Thanks to this assumption and without loss of generality the continuous time interval [0,T] can be discretized in sufficient number U of subintervals

I u = [t u-1 -t u [, 0 = t 0 < t 1 < • • • < t U = T , that
will be then clustered. The number of interactions between i and j on the considered time partition I u is summarized by X iju and is defined as:

X iju := X ij (t u ) -X ij (t u-1 ), ∀(i, j, u).
We introduce a tensor X = {X iju } iju with dimensionality N × P × U . To model the membership to time clusters, a new latent variable s is introduced, in particular s u = c if the time interval I u belongs to the time cluster D c . We assume that s follows a multinomial distribution:

p(s|δ) = C c=1 δ |Dc| c , ( 4
)
where δ c = P{s u = c}; Once these additional assumpions have been made, we can rewrite Eq. ( 3) considering that the intensity functions are stepwise constant on each time cluster D c . Thus:

X iju |z ik w j s uc = 1 ∼ P(λ k c ∆ u ) (5)
where ∆ u indicates the length of the interval I u that is usually constant, ∆ u = ∆. Moreover, we can set ∆ u = 1 without loss of generality.

Likelihood and model inference

From Eq. ( 5), it holds that:

p(X iju |z ik w jl s uc = 1, λ k c ) = (λ klc ) Xiju X iju ! exp (-λ klc )
(6) Therefore, we can introduce the K × L × C tensor λ, identified by the triplet (i, j, u) and whose elements are denoted as λ k c . At this point it is possible to write the complete data likelihood of the model, identified by the following equation: (X|z, w, s, λ) (7) Looking at the right hand side of the Eq. ( 7), we can notice that p(z|γ), p(w|ρ) and p(s|δ) have been defined in the previous section respectively by the Eqs. (1), ( 2) and (4). The joint distribution of X, given z, w, and s, can be easily obtained from Eq. ( 6) by independence:

p(X, z, w, s|γ, ρ, δ, λ) = p(z|γ)•p(w|ρ)•p(s|δ)•p
p(X|z, w, s, λ) = k, ,c (λ k c ) R k c P k c exp (-|A k ||B ||D c |λ k c ) (8) where R k c = N i=1 P j=1 U u=1 z ik w j s uc X iju
The Dynamic Latent Block Model for Sparse and Evolving Count Matrices

P k c = N i=1 P j=1 U u=1 (z ik w j s uc X iju )!
Denote by θ the set of all model parameters, i.e. θ = (γ, ρ, δ, λ), the log-likelihood can be written as:

(θ; X) = z w c log p(X, z, w, s|θ) (9)

Model inference

As usual, we look for a way to maximize the log-likelihood in order to obtain the estimation of θ. In the co-clustering case, the EM algorithm is computationally infeasible. In this work, we have chosen to use a different inference strategy than the one used in [START_REF] Corneli | Block modelling in dynamic networks with non-homogeneous poisson processes and exact icl[END_REF] that relies on a maximization, through a greedy search algorithm, of the derived exact integrated classification likelihood criterion.

The inference strategy we use here for dLBM is known as SEM-Gibbs, proposed by [START_REF] Keribin | Estimation d'un modèle à blocs latents par l'algorithme sem[END_REF] and exploited, for instance, by [START_REF] Bouveyron | The functional latent block model for the co-clustering of electricity consumption curves[END_REF] in the functional latent block model (funLBM). During the SE step the algorithm evaluates the posterior probabilities using the current values for the parameters, while during the M step a new estimation of the model parameters is made. Thanks to the Gibbs Sampling, in the SE step a partition for z, w and s is generated without computing the joint distribution. The algorithm starts with initial values for the parameter set θ (0) , the column clusters w (0) and the time clusters s (0) . Regarding the burn-in period, after a certain number of iterations of the algorithm, we can obtain the final parameters estimation by computing the mean of the sampled distribution. The optimal values for z, w and s are estimated by the mode of their sample distributions.

Model selection

Up to now, we have assumed that the exact number of row clusters (K), column clusters (L) and time clusters (C) to be included in the algorithm were known. However, for real data sets this assumption is unrealistic. For this reason, our purpose in this section is to define a model selection criterion that can automatically identify the optimal number of clusters that compose a data set. The model selection approach is considered. We propose to rely on the ICL (Integrated Completed Likelihood, [START_REF] Biernacki | Assessing a mixture model for clustering with the integrated com-pleted likelihood[END_REF]) criterion to approximate the complete-data integrated loglikelihood. We derived the formulation of the ICL criterion for the model proposed above:

ICL(K, L, C) = log p(X, ẑ, ŵ, ŝ; θ) - K -1 2 log n+ - L -1 2 log p - C -1 2 log u - KLC 2 log(npu) (10)
The triplet ( K, L, Ĉ) that leads to the highest value for the ICL is considered as the most correct for those data.

Analysis of the Amazon fine foods dataset

This section focuses on a real dataset consisting of reviews of fine foods from Amazon. The dataset can be freely downloaded at https://snap.stanford. edu/data/web-FineFoods.html. A time horizon of 10 years is considered, up to October 2012. In the original dataset, the number of reviews reported is 568,464 and each row corresponds to one review. Some additional information is reported for each review: the user/product numerical identifiers, a summary of the review and a rating attributed to the product by the user. The rating is expressed via an integer number spanning from 1 (very bad) to 5 (very good). To focus on the most meaningful part of the data, we only considered the users reviewing more than 30 times and the products being reviewed more than 55 times.

In the Amazon Fine Foods dataset, we consider one month as the dimension of a single time interval as ∆ u . The distribution of the observations during the considered time period is shown in Figure 1. To be able to run our algorithm, we need to group the data building a sparse array with N rows, P columns and U slices. Thus, we end up with a 235 × 151 × 52 cube X, where each user is represented by a row, each product is represented by a column and each time interval is represented by a slice of the cube. Each entry of the cube represents an interaction between a reviewer and a product on a specific time interval. In the final data set, the rate of missing values is 0.98%. Once the array has been built, we can run the model using the SEM-Gibbs algorithm to identify the optimal number of K row clusters (users), L column clusters (products) and C time clusters. We run the algorithm over 48 different models, with rows and columns groups ranging from 2 to 5 and time clusters groups ranging from 2 to 4. To run this In Figure 2, one can observe the reorganized incidence matrix according to row and column clusters, and this for each time cluster (each panel represents a different time cluster). To this end, we permuted the rows and the columns of the incidence matrix thanks to the estimates ẑ and ŵ in such a way that nearby rows (columns) belong to the same cluster of rows (columns). The blocks are also delimited by the black dashed lines.

One can notice that time cluster 1 contains few and sparse interactions, without a clear structure regarding the blocks. This means that, for time periods belonging to this time cluster, the users comment the product on an irregular basis and almost randomly. Conversely, in time cluster 2, there is a clear structure regarding the blocks: all users have a clear tendency to comment and buy products of the first column clusters whereas they do not consider at all products of the two other column clusters (2 and 3). It can be also noticed that users of the firs row cluster (bottom row blocks) have a higher probability to comment products of the first column cluster than users from the second row cluster. The third time cluster is quite similar to the 2nd time cluster in term of block structure, but the interaction intensity is clearly lower. Finally, time cluster 4 shows a very specific structure since, this time, the first group of product does not receive much attention whereas the products of the second column cluster are frequently commented by all users and the ones of the third column cluster are very intensively reviewed by the users of the 2nd row cluster (top row block). These analyses are also summarised in Figure 2 which shows the estimated valued for the tensor λ.

Conclusion

We considered the problem of co-clustering count matrices with a high level of missing values that may evolve along the time. To this end, we introduce a generative model, named dynamic latent block model (dLBM), which extends the classical binary latent block model to the dynamic case. The modeling of the dynamic time framework in a continuous time relies on a non-homogeneous Poisson process, with a latent partition of time intervals. Inference is done using a SEM-Gibbs algorithm and the ICL criterion is used for model selection. The dLBM algorithm was applied to a realworld data set from Amazon with a extremely high level of missing values. In this context, dLBM provided meaningful segmentation of rows, columns and time.

  1 and |D c | represents the number of time intervals in the cluster D c .

Figure 1 .

 1 Figure 1. Distribution of users and products before running the algorithm

Figure 2 .

 2 Figure 2. Reorganized incidence matrix for each time cluster. Rows and columns clusters are delimited by the dashed lines while the colored dots marks an interaction (i.e. review) between a user and a product.

Figure 3 .

 3 Figure 3. Estimated parameters of the probability distribution of interactions between users and products, according to time clusters

Table 1 ,

 1 the ICL selects as the best dLBM model the one with 2 groups of users, 3 groups of products and 4 time clusters.

	Rank K L C	ICL
	1	2 3 4 -32509.56
	2	2 5 2 -32916.66
	3	2 4 2 -32919.41
	4	4 5 2 -32957.24
	5	4 2 2 -32978.14

Table 1 .

 1 Selection of the most appropriate model for the Amazon Fine Foods data.