Emmanouil Benetos
email: emmanouilb@eecs.qmul.ac.uk

Mathieu Lagrange
email: mathieu.lagrange@ircam.fr

Simon Dixon
email: simond@eecs.qmul.ac.uk

Characterisation of Acoustic Scenes using a Temporally Constrained Shit-Invariant Model

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INTRODUCTION

The problem of modeling acoustic scenes is one of the most challenging tasks in the computational auditory scene analysis (CASA) field [START_REF]Computational auditory scene analysis: Principles, algorithms and applications[END_REF]. It is closely related to the problem of detecting and classifying acoustic events within a scene, and has numerous applications in audio processing. In the case of scene categorisation or characterization, we are interested in specifying the environment of the recording, which is informed by the types of events that are present within the scene of interest. The problem is especially challenging in the case of a real-world scenario with an unlimited set of events which could also overlap in time. It should be noted that event detection and scene categorisation is easily achieved by humans, even in the case of multiple overlapping events.

The literature in this domain is quite vast and we shall now describe two references that consider a technical approach that is close to the one considered in this paper. Mesaros et al. [START_REF] Mesaros | Latent semantic analysis in sound event detection[END_REF] proposed a system for sound event detection which employed probabilistic latent semantic analysis (PLSA) for separating and detecting overlapping events. PLSA (or PLCA, as called in this work) is a factorization technique closely linked to non-negative matrix factorization (NMF). The system was tested in a supervised scenario using a dataset of 103 recordings classified into 10 different scenes, containing events from 61 classes.

In [START_REF] Cotton | Spectral Vs. spectro-temporal features for acoustic event detection[END_REF], Cotton and Ellis utilised the convolutive NMF algorithm for non-overlapping event detection. A comparison was made between convolutive NMF (which learns spectro-temporal basis matrices) with a frame-based approach using Mel-frequency cepstral coefficients (MFCCs). Experiments performed on a dataset collected under the CHIL project, consisting of 16 different event classes, showed that a combination of the convolutive NMF system and the frame-based system yielded the best results. It should be noted that the convolutive NMF algorithm is closely related to the shift-invariant probabilistic latent component analysis (SIPLCA) algorithm that is used in the present paper.

In some cases, the salient events that characterise the scene are not known a priori, or may be hard to learn from training data due to the large discrepancy between two acoustic realizations of the same event. For example, in the last decades a wide range of scientific projects designed and put into service massive monitoring devices based on hydrophone or microphone arrays1 . Among this vast amount of data, one can seek for known acoustic events or alternatively try to discover events of unknown type. The latter leads us to an unsupervised formulation of the scene description problem, where we have only a few loose assumptions about the events of interest and we want the algorithm to be able to extract in an unsupervised manner the events that semantically describe the scene.

Following this approach, Cauchi [START_REF] Cauchi | Non-negative matrix factorisation applied to auditory scenes classification[END_REF] proposed a method for classifying auditory scenes in an unsupervised manner using sparse non-negative matrix factorization. After extracting spectral basis vectors from acoustic scenes, each basis is converted into MFCCs for compactness. A distance metric is defined for measuring the difference between extracted dictionaries from different scenes. Evaluation is performed on a corpus of 66 recordings taken from several train stations [START_REF] Tardieu | Perceptual study of soundscapes in train stations[END_REF], originally created for a perceptual study on acoustic scene categorisation, resulting in six acoustic scene classes. Experiments made by comparing the sparse NMF with a bag-of-features approach from [START_REF] Aucouturier | The bag-offrames approach to audio pattern recognition: a sufficient model for urban soundscapes but not for polyphonic music[END_REF] showed that the NMF algorithm is able to successfully extract salient events within an acoustic scene.

In the present paper, we build upon this work and propose a method for modeling and classifying acoustic scenes in an unsupervised manner using shift-invariant probabilistic models. The shift-invariant probabilistic latent component analysis (SIPLCA) algorithm [START_REF] Smaragdis | Shift-invariant probabilistic latent component analysis[END_REF] is used in order to extract time-frequency basis matrices from log-frequency spectrograms. In addition, an algorithm is proposed for incorporating temporal constraints to the SIPLCA algorithm using component-wise hidden Markov models (HMMs). These temporal constraints control the occurrence of each acoustic event within a scene using on/off HMMs. The extracted timefrequency basis matrices are afterwards converted to a compact representation using cepstral coefficients. A distance metric is defined for comparing the extracted dictionaries between different acoustic scenes. Evaluation is performed on the same dataset of train station recordings as in [START_REF] Cauchi | Non-negative matrix factorisation applied to auditory scenes classification[END_REF]. Results using ranking and classification measures show that the proposed SIPLCA models outperform state-of-the art approaches for the same experiment, such as non-negative matrix factorization [START_REF] Cauchi | Non-negative matrix factorisation applied to auditory scenes classification[END_REF] and a bag-of-frames approach with Gaussian mixture models [START_REF] Aucouturier | The bag-offrames approach to audio pattern recognition: a sufficient model for urban soundscapes but not for polyphonic music[END_REF]. In addition, it is shown that incorporating temporal constraints regarding the activation of acoustic scenes, as well as incorporating sparsity constraints on the same activation can lead to more informative basis vectors and thus to improved performance.

The outline of the paper is as follows. The shift-invariant probabilistic latent component analysis method is presented in Section 2. Section 3 presents the proposed temporally-constrained model and the computation of the distance between acoustic scenes. The employed dataset of train station soundscapes, the utilised metrics, and the experimental results compared to other state-of-theart methods are shown in Section 4. Finally, conclusions are drawn and future directions are indicated in Section 5.

SHIFT-INVARIANT PLCA

Shift-invariant probabilistic latent component analysis (SIPLCA) was proposed in [START_REF] Smaragdis | Shift-invariant probabilistic latent component analysis[END_REF] for extracting shifted structures from nonnegative data. It is a convolutive extension of the probabilistic latent component analysis (PLCA) algorithm, that was proposed by Smaragdis et al. [START_REF] Smaragdis | A probabilistic latent variable model for acoustic modeling[END_REF]. As PLCA can be viewed as a probabilistic formulation of the non-negative matrix factorization (NMF) algorithm, SIPLCA can be viewed as a probabilistic formulation of the convolutive NMF algorithm [START_REF] O'grady | Convolutive nonnegative matrix factorisation with a sparseness constraint[END_REF] using the Kullback-Leibler divergence as a cost function. SIPLCA has been used in the past for pitch tracking [START_REF] Mysore | Relative pitch estimation of multiple instruments[END_REF] and automatic transcription of polyphonic music [START_REF] Benetos | Multiple-instrument polyphonic music transcription using a convolutive probabilistic model[END_REF].

The SIPLCA algorithm can support the extraction of a onedimensional basis from a spectrogram or the extraction of a timefrequency patch. In the present work, we will employ the latter SIPLCA model for extracting 2-dimensional basis matrices. The model takes as an input a normalized spectrogram Vω,t and approximates it as a bivariate distribution P (ω, t), where ω is the frequency index and t the time index. P (ω, t) is decomposed as a series of time-frequency patches convolved over time. The model is formulated as follows:

Vω,t ≈ P (ω, t) = X z P (z)P (ω, τ |z) * τ P (t|z) = X z P (z) X τ P (ω, τ |z)P (t -τ |z) (1)
where P (ω, τ |z) is the time-frequency patch for the z-th component, P (z) is the component prior, and P (t|z) is the activation for each component. The unknown model parameters can be estimated using the expectation-maximization (EM) algorithm [START_REF] Dempster | Maximum likelihood from incomplete data via the EM algorithm[END_REF]:

• Expectation step: • Maximization step:

P (z, τ |ω, t) = P (z)P (ω, τ |z)P (t -τ |z) P z P τ P (z)P (ω, τ |z)P (t -τ |z) (2)
P (z) = P ω,t,τ Vω,tP (z, τ |ω, t) P z,ω,t,τ Vω,tP (z, τ |ω, t) (3)
P (ω, τ |z) = P t Vω,tP (z, τ |ω, t) P ω,τ,t Vω,tP (z, τ |ω, t) (4)
P (t|z) = P ω,τ Vω,t+τ P (z, τ |ω, t + τ ) P t,ω,τ Vω,t+τ P (z, τ |ω, t + τ ) (5)
Equation ( 2) is computed through the model of (1) using Bayes' theorem and expresses the posterior of the unknown variables over the known data. The unknown matrices are initialized with random values. The update rules of (2)-( 5) are iterated until convergence. An example of the SIPLCA algorithm is given in Fig. 1, where SIPLCA is applied to a recording of footsteps with z = 2. The activations P (t|z) of the footsteps are clearly seen as spikes.

In [START_REF] Smaragdis | Relative-pitch tracking of multiple arbitary sounds[END_REF], sparsity constraints are applied to the model in order to provide as meaningful solutions as possible. The sparsity constraints are applied using an entropic prior, by modifying the update equations in the maximization step. In the present work, we will encourage sparsity on the component activation P (t|z) in order to derive informative basis matrices.

PROPOSED METHOD

Motivation

The motivation behind the model proposed in this paper is to include another level of temporality, which controls the appearance of the time-frequency patches in a recording. These temporal constraints can be supported by incorporating HMMs within the SIPLCA model. Ideally, the component activation function would consist of zeros in case of inactivity and ones at the time instants where an event would appear. Each HMM can represent a certain component, which would be represented using a two-state, on/off model. This on/off model would serve as an event indicator function, which would enforce temporal constraints in the auditory scene activation matrix. Thus, in this case we propose a novel model which supports time-frequency patches for auditory scene characterization and also controls the temporal succession of these scenes.

This work will extend the temporally-constrained convolutive probabilistic model for pitch detection presented in [START_REF] Benetos | A temporally-constrained convolutive probabilistic model for pitch detection[END_REF], which utilised shift-invariance over log-frequency for spectra instead of performing shift-invariance over time for time-frequency basis as in this work. These models which combine spectral factorization techniques with HMMs were first introduced in [START_REF] Mysore | A non-negative framework for joint modeling of spectral structure and temporal dynamics in sound mixtures[END_REF], where the non-negative HMM algorithm was proposed.

HMM-constrained Shift-invariant PLCA

This proposed temporally-constrained model takes as input a normalized spectrogram Vω,t and decomposes it as a series of timefrequency patches. Also produced is a component activation matrix, as well as component priors. The activation of a each acoustic component is controlled via a 2-state HMM. The model can be formulated as:

Vω,t ≈ P (ω, t) = X z P (z) X q (z) t P (ω, τ |z) * τ P (t|z)P (q (z) t |t) (6)
where q (z) t is the state sequence for the z-th component, z = 1, . . . , Z. Since P q (z) t P (q (z)

t |t) = 1, we can revert to the nontemporally constrained model of the previous section. Thus in the model, the desired source activation is given by P (z|t)P (q

(z) t = 1|t).
The activation sequence for each component is constrained using a corresponding HMM, which is based on the produced source activation P (z, t) = P (z)P (t|z). In terms of the activations, the component-wise HMMs can be expressed as:

P (z) = X q(z) P (q (z) 1 ) Y t P (q (z) t+1 |q (z) t ) Y t Pt(zt|q (z) t ) (7)
where z refers to the sequence of activations for a given component z, P (q (z) 1 ) is the prior probability, P (q

(z) t+1 |q (z)
t ) is the transition matrix for the z-th component, and Pt(zt|q

(z)
t ) is the observation probability (zt refers to the activation at frame t). The observation probability for an active component is defined using a sigmoid curve:

Pt(zt|q (z) t = 1) = 1 1 + e -P (z,t)-λ (8)
where λ is a parameter that controls the component activation (a high value will lead to a low observation probability, leading to an 'off' state). The formulation of the observation function is similar to the one used for multiple note tracking in [START_REF] Poliner | A discriminative model for polyphonic piano transcription[END_REF].

As in the model of Section 2, the unknown parameters in the model can be estimated using the EM algorithm [START_REF] Dempster | Maximum likelihood from incomplete data via the EM algorithm[END_REF]. For the Expectation step, we compute the posterior for all the hidden variables:

P (z, τ, q (1) t , . . . , q (Z) t |z, ω, t) = P (q (1) t , . . . , q (Z) t |z)P (z, τ |q (1) t , . . . , q (Z) t , ω, t) (9)
Since we are utilising independent HMMs, the joint probability for all hidden source states is given by:

Pt(q (1)
t , . . . , q

(Z) t |z) = Z Y z=1 Pt(q (z) t |z) (10)
where

Pt(q (z) t |z) = Pt(z, q (z) t ) P q (z) t Pt(z, q (z) t ) = αt(q (z) t )βt(q (z) t ) P q (z) t αt(q (z) t )βt(q (z) t )
(11) and αt(q (z) t ), βt(q (z) t ) are the forward and backward variables for the z-th HMM [START_REF] Rabiner | A tutorial on hidden Markov models and selected applications in speech recognition[END_REF], which can be computed recursively:

α1(q1) = P (z1|q1)P (q1) αt+1(qt+1) = " X qt P (qt+1|qt)αt(qt) « •Pt+1(zt+1|qt+1) (12)
βT (qT ) = 1 βt(qt) = X q t+1 βt+1(qt+1)P (qt+1|qt)Pt+1(zt+1|qt+1) (13)
The second term of ( 9) can be computed using Bayes' theorem:

P (z, τ |q (1)
t , . . . , q

(Z) t
, ω, t) = P (z, τ |ω, t) = P (z)P (ω, τ |z)P (tτ |z)

P z P τ P (z)P (ω, τ |z)P (t -τ |z)|t) (14)
Finally, the posterior for the component transition matrix is given by:

Pt(qt, qt+1|z) = αt(qt)P (qt+1|qt)βt+1(qt+1)Pt(zt+1|qt+1) P qt,q t+1 αt(qt)P (qt+1|qt)βt+1(qt+1)Pt(zt+1|qt+1) (15)
For the Maximization step, the update rules for estimating the unknown parameters are:

P (z) = P ω,τ,t P q (z) t
Vω,tP (z, τ, q

(1) t , . . . , q

(Z) t |ω, t) P z,ω,τ,t P q (z) t
Vω,tP (z, τ, q

(1) t , . . . , q

(Z) t |ω, t) (16)
P (ω, τ |z) = P t P q (z) t
Vω,tP (z, τ, q

t , . . . , q

(Z) t |ω, t) P ω,τ,t P q (z) t
Vω,tP (z, τ, q

t , . . . , q

(Z) t |ω, t) (17)
P (t|z) = P ω,τ P q (z) t
Vω,t+τ P (z, τ, q

t , . . . , q

(Z) t |ω, t + τ ) P t,ω,τ P q (z) t
Vω,t+τ P (z, τ, q

t , . . . , q

(Z) t |ω, t + τ ) (18)
P (q

(z) t+1 |q (z) t ) = P t P (q (z) t , q (z) t+1 |z) P q (z) t+1 P t P (q (z) t , q (z) t+1 |z) (19)
P (q

(z) 1 ) = P1(q (z) 1 |z) (20)
where

P q (z) t = P q (1) t • • • P q (Z) t
. Eq. ( 20) updates the component prior using the posterior of eq. [START_REF] Benetos | Multiple-instrument polyphonic music transcription using a convolutive probabilistic model[END_REF]. Thus, the update equations of the proposed model are a combination of the SIPLCA update rules and the forward-backward HMM algorithm. The final event activation is given by the activation for each component given by the model and the probability for an active state for the corresponding component: P (z, t, q (z) t = 1) = P (z)P (t|z)P (q As in the SIPLCA model of Section 2, sparsity constraints are applied to P (t|z) using the entropic prior of [START_REF] Smaragdis | Relative-pitch tracking of multiple arbitary sounds[END_REF] in order to obtain a sparse component activation. In Fig. 3, extracted time-frequency basis matrices can be seen, from a recording employed for evaluation (described in Section 4) using the proposed method with z = 5. Components corresponding to different acoustic events can be seen in the figure. For all the experiments performed in this paper, the length of each basis has been set to 400ms.

(z) t = 1|t) (21)

Acoustic Scene Distance

For computing the distance between acoustic scenes, we first compute the constant-Q transform [START_REF] Schörkhuber | Constant-Q transform toolbox for music processing[END_REF] of each 44.1 kHz recording with a log-frequency resolution of 5 bins per octave and an 8octave span with 27.5 Hz set as the lowest frequency. The step size is set to 40 ms. Afterwards, time-frequency basis matrices are extracted using the proposed HMM-constrained SIPLCA algorithm of Section 3.2 with R = {10, 25, 50} bases and λ = 0.005 (the value was set after experimentation). Sparsity was enforced to P (t|z) using an entropic prior method of [START_REF] Smaragdis | Relative-pitch tracking of multiple arbitary sounds[END_REF] with sparsity parameter values sH = {0, 0.1, 0.2, 0.5}. In all cases the length of each basis is set to 400 ms.

For each basis W = P (ω, τ |z), very small values are replaced by the median value of W . Afterwards, a vector of 13 cepstral coefficients is computed for each basis frame, in order to result in a compact representation for computational speed purposes. In order to convert a vector w[k](k = 1, . . . , K) into cepstral coefficients, we employ the formula presented in [START_REF] Brown | Computer identification of musical instruments using pattern recognition with cepstral coefficients as features[END_REF]:

ci = K X k=1 log(w[k]) cos " i " k - 1 2 « π K « ( 22
)
where i = 1, . . . , 13. Each vector of cepstral coefficients is then normalized to the range [0,1] region. Thus, the first coefficient that corresponds to the DC component of the signal is dropped.

Finally, for each time-frequency basis, the coefficients are summed together over time, thus resulting in a single vector representing a basis.

For computing the distance between a scene l and a scene m, we employ the same steps as in [START_REF] Cauchi | Non-negative matrix factorisation applied to auditory scenes classification[END_REF]. Firstly, we compute the element wise distance between a basis W l (r), r = 1, . . . , R and the nearest basis of dictionary Wm:

dr(l, m) = min j∈[1,R] ||W l (r) -Wm(j)|| (23)
The final distance between two acoustic scenes is defined as:

D(l, m) = R X r=1 dr(l, m) + dr(m, l) (24)
Equation ( 24) is formulated in order for the distance measure between two scenes to be symmetric. In the end, the acoustic scene distance matrix D is used for evaluation. We acknowledge that quantifying the distance between two basis vectors by considering the Euclidean distance of their time average most probably leads to a loss of descriptive power of our model. This choice is made for tractability purposes. Indeed, for the corpus used in this study and 50 bases per item, building the matrix D involves comparing about 10 6 bases. Finding an efficient way of considering the time axis during the distance computation is left for future research.

EVALUATION

Dataset

For the acoustic scene classification experiments we employed the dataset created by J. Tardieu [START_REF] Tardieu | Perceptual study of soundscapes in train stations[END_REF]. The dataset was originally created for a perceptual study on free-and forced-choice recognition of acoustic scenes by humans. It contains 66 44.1 kHz files recorded in 6 different train stations (Avignon, Bordeaux, Lille Flandres, Nantes, Paris Est, Rennes). Each file is classified into a 'space', which corresponds to the location this file was recorded: platforms, halls, corridors, waiting room, ticket offices, shops. The recordings contain numerous overlapping acoustic events, making even human scene classification a nontrivial task. In Table 1, the class distribution for the employed dataset can be seen. In addition to the ground truth included for each recording, an additional scene label is included as a result of the forced-categorisation perceptual study performed in [START_REF] Tardieu | Perceptual study of soundscapes in train stations[END_REF].

Scene

Platform Hall Corridor Waiting Ticket Office Shop No. Samples 10 16 12 13 10 5

Table 1: Class distribution in the employed dataset of acoustic scenes.

Evaluation metrics

For evaluation, we employed the same set of metrics that were used in [START_REF] Cauchi | Non-negative matrix factorisation applied to auditory scenes classification[END_REF] for the same experiment, namely the mean average precision (MAP), the 5-precision, and the classification accuracy of a nearest neighbour classifier. The MAP and 5-precision metrics are utilised for ranked retrieval results, where in this case the ranking is given by the values of the distance matrix D. MAP is able to provide a single-figure metric across recall levels and can describe the global behaviour of the system. It is computed using the average precision, which is the average of the precision obtained for the set of top n documents existing after each relevant document is retrieved. The 5-precision is the precision at rank 5 (which corresponds to the number of samples in the smallest class), which describes the system performance at a local scale.

Regarding the classification accuracy metric, for each row of D we apply the k-nearest neighbour classifier with 11 neighbours, which corresponds to the average number of samples per class.

Results

Acoustic scene classification experiments were performed using the SIPLCA algorithm of [START_REF] Smaragdis | Shift-invariant probabilistic latent component analysis[END_REF] and the proposed SIPLCA algorithm with temporal constraints (TCSIPLCA). Comparative results are also reported using a bag-of-frames (BOF) approach of [START_REF] Aucouturier | The bag-offrames approach to audio pattern recognition: a sufficient model for urban soundscapes but not for polyphonic music[END_REF] reported in [START_REF] Cauchi | Non-negative matrix factorisation applied to auditory scenes classification[END_REF]. The BOF method computes several audio features which are fed to a Gaussian mixture model (GMM) classifier. The NMF method of [START_REF] Cauchi | Non-negative matrix factorisation applied to auditory scenes classification[END_REF] was also implemented and tested. Results are also compared with the human perception experiment reported in [START_REF] Tardieu | Perceptual study of soundscapes in train stations[END_REF]. Experiments were performed using different dictionary sizes R and sparsity parameters sH (details on the range of values can be seen in Section 3.3).

The best results using each employed classifier are presented in Table 2. It can be seen that the proposed temporally-constrained SIPLCA model outperforms all other classifiers using both metrics, apart from the human forced categorisation experiment. The proposed method slightly outperforms the standard SIPLCA algorithm, which in turn outperforms the NMF algorithm. It can also be seen that the BOF method is clearly not suitable for such experiment, since the audio features employed in this method are more appropriate for non-overlapping events, whereas the dataset that is utilised contains concurrent events. However, it can be seen that the human categorisation experiment from [START_REF] Tardieu | Perceptual study of soundscapes in train stations[END_REF] outperforms all other approaches.

More detailed results for the SIPLCA algorithm using different sparsity parameter values and a different number of extracted bases (R) can be seen in Fig. 4. It can be seen that in all cases, enforcing sparsity improves performance. It can also be seen that the best performance is reported for R = 25, although the performance of the system using R = 50 improves when greater sparsity on P (t|z) is encouraged. Detailed results for the proposed TCSIPLCA method can be seen in Fig. 5, using different dictionary sizes and sparsity values. It can be seen that the performance reaches a peak when sH = 0.2, for the case of R = 25.

Classifier

MAP 5-Precision Human Perception [START_REF] Tardieu | Perceptual study of soundscapes in train stations[END_REF] 0.62 0.73 Random 0.25 0.18 BOF [START_REF] Aucouturier | The bag-offrames approach to audio pattern recognition: a sufficient model for urban soundscapes but not for polyphonic music[END_REF] 0.24 0.18 NMF (R = 50, sH = 0.99) 0.32 0.29 SIPLCA (R = 25, sH = 0.2) 0.33 0.35 TCSIPLCA (R = 25, sH = 0.2) 0.34 0.36 When using a dictionary size of R = 50, the performance of the proposed method is slightly decreased. Thus, selecting the appropriate number of components is important in the performance of the proposed method, since using too many components will lead to a parts-based representation which in the unsupervised case will lead to non representative dictionaries. Likewise, selecting too few bases will lead to a less descriptive model of the input signal. Regarding classification accuracy using 11-nearest neighbours, results are shown in Table 3. Again, the TCSIPLCA method outperforms all the other automatic approaches. In this case however, the NMF approach from [START_REF] Cauchi | Non-negative matrix factorisation applied to auditory scenes classification[END_REF] outperforms the SIPLCA algorithm by 0.5%. For the TCSIPLCA algorithm, the best performance is again reported for sH = 0.2, while for the NMF approach the best performance is reported for sH = 0. It should also be noted that regarding dictionary size, the best results are reported for R = 50. Detailed classification results using the SIPLCA and TCSIPLCA methods can be seen in Figures 6 and7, respectively.

It should also be noted that some experiments were performed by selecting only basis vectors that correspond to a sparse activation P (t|z). In the PLCA domain, the sparseness criterion can be given by maximizing the l2 norm as in [START_REF] Smaragdis | Polyphonic pitch tracking by example[END_REF], due to the fact that all elements of the activation matrix take values between 0 and 1. However, the performance of the SIPLCA and TCSIPLCA algorithms in fact decreased slightly when selecting only the basis vectors that corresponded to the sparsest activations. This issue may be addressed in the future by enforcing sparsity only to certain components that represent salient events and keeping the rest of the components (which could represent noise) without enforc- ing sparsity.

CONCLUSIONS

In this work we proposed a method for modeling and classifying acoustic scenes using shift-invariant probabilistic methods. The shift-invariant probabilistic latent component analysis algorithm was utilised for learning time-frequency basis matrices from an input acoustic signal in an unsupervised manner. An algorithm was proposed for incorporating temporal constraints to the SIPLCA model using hidden Markov models, in order to constrain the activation of each event in the signal. In the classification stage, each extracted time-frequency basis is converted into a compact vector of cepstral coefficients for computational speed purposes. The employed dataset consisted of recordings taken from six types of scenes at different train stations. Comparative experiments were performed using a standard non-negative matrix factorization approach, as well as a bag-of-frames algorithm which is based on computing audio features. Results show that using shift-invariant models for learning time-frequency basis matrices improves classification performance. Moreover, incorporating temporal constraints in the SIPLCA model as well as enforcing sparsity constraints in the component activation resulted in improved classification performance. However, the classification performance of the proposed computational methods is still significantly lower than the human forced categorisation task presented in [START_REF] Tardieu | Perceptual study of soundscapes in train stations[END_REF]. We acknowledge that this performance is in our case an upper bound that may not even be reached by purely data-driven methods since humans most probably make extensive use of prior knowledge but the significant gap between the human and computational performances indicates that there is potentially room for improvement on the computational side.

In order to improve spectrogram factorization techniques such as NMF and SIPLCA, additional constraints and knowledge need to be incorporated into the models. A hierarchical model which would consist of event classes and component subclasses would result in a richer model, but would also require prior information on the shape of each event in order to result in meaningful basis matrices. Prior information can be provided by utilising training

Classifier

Accuracy % Human Perception [START_REF] Tardieu | Perceptual study of soundscapes in train stations[END_REF] 54.8% Random 16.6% BOF [START_REF] Aucouturier | The bag-offrames approach to audio pattern recognition: a sufficient model for urban soundscapes but not for polyphonic music[END_REF] 19.7% NMF (R = 50, sH = 0) 34.1% SIPLCA (R = 25, sH = 0.5) 33.6% TCSIPLCA (R = 50, sH = 0.2) 35.0% samples of non-overlapping acoustic events. Also, an additional sparseness constraint could be imposed in the activation matrix, in order to control the number of overlapping components present in the signal (instead of enforcing sparsity as in the present work). In addition, instead of using a first-order Markov model for imposing temporal constraints, a more complex algorithm which would be able to model the duration of each event, such as a semi-Markov model [START_REF] Yu | Hidden semi-Markov models[END_REF] can be employed. Finally, finding an efficient way of comparing extracted time frequency patches is also important. In this respect, we believe that lower bounding approaches to the dynamic time warping (DTW) technique are of interest [START_REF] Zhang | An inner-product lower-bound estimate for dynamic time warping[END_REF].

Figure 1 :

 1 Figure 1: SIPLCA applied to a sequence of footsteps (z = 2). Top left: input CQT spectrogram, right: extracted basis matrices, bottom: extracted component activations.

Figure 2 :

 2 Figure 2: Diagram for the proposed acoustic scene classification system.

Figure 3 :

 3 Figure 3: Extracted time-frequency basis matrices using the proposed model.

Figure 4 :

 4 Figure 4: Acoustic scene classification results (MAP) using the SIPLCA algorithm with different sparsity parameters and dictionary size (R).

Figure 5 :

 5 Figure 5: Acoustic scene classification results (MAP) using the TCSIPLCA algorithm with different sparsity parameters and dictionary size (R).

Figure 6 :

 6 Figure 6: Classification accuracy (%) using the SIPLCA algorithm with different sparsity parameters and dictionary size (R).

Figure 7 :

 7 Figure 7: Classification accuracy (%) using the TCSIPLCA algorithm with different sparsity parameters and dictionary size (R).

Table 2 :

 2 Best MAP and 5-precision results for each model.

		0.35
		0.34
			R = 10
		0.33	R = 25
			R = 50
		0.32
		0.31
	MAP	0.3
		0.29
		0.28
		0.27
		0.26
		0	0.1	0.2	0.5
			sH

Table 3 :

 3 Best classification accuracy for each model.

See for an example: http://www.neptunecanada.ca

The first author is funded by a Westfield Trust research studentship (Queen Mary University of London) and performed part of this work while visiting IRCAM. The second author is partly funded by ANR-11-JS03-005-01


Lagrange Mathieu
email: lagrange@ircam.fr

Gustavo Luis

Martins
email: lmartins@porto.ucp.pt

George Tzanetakis

CLUSTER AWARE NORMALIZATION FOR ENHANCING AUDIO SIMILARITY

Keywords: distance normalization, information retrieval, kernel-based clustering

An important task in Music Information Retrieval is content-based similarity retrieval in which given a query music track, a set of tracks that are similar in terms of musical content are retrieved. A variety of audio features that attempt to model different aspects of the music have been proposed. In most cases the resulting audio feature vector used to represent each music track is high dimensional. It has been observed that high dimensional music similarity spaces exhibit some anomalies: hubs which are tracks that are similar to many other tracks, and orphans which are tracks that are not similar to most other tracks. These anomalies are an artifact of the high dimensional representation rather than actually based on the musical content. In this work we describe a distance normalization method that is shown to reduce the number of hubs and orphans. It is based on post-processing the similarity matrix that encodes the pair-wise track similarities and utilizes clustering to adapt the distance normalization to the local structure of the feature space.

INTRODUCTION

Searching large databases for objects that have similar properties is a key task in many data mining applications. These objects are typically represented as a series of scalar features and therefore can be viewed as points in a vector space with dimensionality equal to the number of features. Using this representation the search for similar objects reduces to finding vectors that are neighbors of the feature vector representing the query object. In some cases, the only information at hand for achieving such a task is the distance between every pair of objects. Unfortunately, this raw information usually lacks consistency. As the dimensionality of the feature space gets higher, some objects get irrelevantly close or far from any other object [START_REF] Radovanovic | Nearest Neighbors in High-Dimensional Data : The Emergence and Influence of Hubs[END_REF][START_REF] Aucouturier | A scale-free distribution of false positives for a large class of audio similarity measures[END_REF]. These objects are respectively coined "hubs" (which are irrelevantly close to many other objects) and "orphans" (which are irrelevantly far to many other objects). Hubs and orphans shall be avoided, as in practice they will respectively be often / never returned by ranking systems. Consequently, reducing them shall also lead to an improvement of precision and recall in ranking-based MIR applications.

Therefore, an alternative approach is to consider local normalization approaches which consider statistics that are computed over a given neighborhood [START_REF] Zelnik | Self-Tuning Spectral Clustering[END_REF]. The main issue is how to define K, i.e the size of the neighborhood to consider for the normalization. In [START_REF] Zelnik | Self-Tuning Spectral Clustering[END_REF], K is set to a unique arbitrarily small number with respect to the cardinality of the set of objects, N , and typically K ∈ [5, 20] << N . It is shown in [START_REF] Lagrange | Adaptive N-Normalization for enhancing Music Similarity[END_REF] that this arbitrary setting is equivalent to the hypothesis that the set of objects is organized in clusters each of cardinality #C l = K, ∀l (where l is the cluster label).

However, these clusters of objects (which correspond to actual classes) may be heterogeneous in size. We therefore propose to consider a normalization factor that is independently set for each object o i , expressed as a function of the cardinality of the class it belongs to

K i = #C l , o i ∈ C l . (1)
The contribution of this paper is twofold. First, we demonstrate that, assuming prior knowledge of the organization of the data in classes/clusters of potentially heterogeneous cardinality, one can enhance several desirable properties of the affinity matrix. That is, the resulting cluster aware local normalization scheme is consistently better than other schemes in terms of accuracy and reversibility improvement. Secondly, we demonstrate that such normalization can be performed in an unsupervised manner, by estimating the cluster organization with the data at hand.

BACKGROUND

Let us consider N objects o i , each described by a set of features f i , upon which an distance matrix D encodes the pairwise distance d ij between each each couple of objects, i and j. It is proposed in [START_REF] Zelnik | Self-Tuning Spectral Clustering[END_REF] to infer from that distance an affinity matrix A ij using a normalization factor specific to each object:

a ij = exp -d 2 ij σ i σ j (2)
where σ i , σ j are the scaling parameters for objects i and j respectively. More precisely, a Local Scaling (LS) is performed in [START_REF] Zelnik | Self-Tuning Spectral Clustering[END_REF], by considering a neighborhood of a given object to normalize its affinity towards the other objects. In this case,

σ i = d ib ( 3
)
where b is the index of the K th nearest neighbor of o i .

Let us consider Equation 2 as the simpler function a = e -d * , where

d * ij = d ij √ σ i σ j (4)
Working directly on the distance matrix allow us to consider an iterative version of this normalization scheme by iteratively processing the resulting distance matrix several times.

DETERMINING K

Local schemes need K (the size of the neighborhood considered for normalization) to be set by the end user. In [START_REF] Zelnik | Self-Tuning Spectral Clustering[END_REF], K is set a priori for convenience to a small value. In the experiments reported in [START_REF] Pohle | Automatically Adapting the Structure of Audio Similarity Spaces[END_REF], the authors observed that, after a given value (K = 25), increasing K did not improve nor decreased significantly the accuracy. Even though such arbitrary setting may be convenient, it is may be desirable to set this value according to some statistics over the dataset at hand, as studied in [START_REF] Lagrange | Unsupervised Accuracy improvment for Cover Song Detection using Spectral Connectivity Network[END_REF]. It has been hypothesized that setting K to a given value is equivalent to assuming that the dataset is roughly organized as set of clusters with cardinality equal to K [START_REF] Lagrange | Unsupervised Accuracy improvment for Cover Song Detection using Spectral Connectivity Network[END_REF]. In fact, and as shown in [START_REF] Lagrange | Adaptive Nnormalization for Enhancing Music Similarity[END_REF], setting K as a low value is harmful as far as accuracy is concerned, and the maximal performance is reached when K is around the number of elements within each class. When dealing with realistic data, several phenomena can influence the optimal K setting. For example the presence of outliers supports considering a smaller K than the number of elements within each class.

PROPOSED APPROACH

We therefore propose to consider an alternate approach that roots the normalization process with perfect or estimated knowledge of the organization of the objects within the dataset.

Assuming knowledge of the class assignments

Instead of considering a fixed size of neighborhood to perform a local scaling of a given distance metric, we propose to consider a neighborhood size K specific for every object in a cluster. Brute force optimization of such sizes is impractical for datasets of reasonable size. So, in order to set this value, we propose to consider the cardinality of the cluster to which the object belongs:

K i = #C l , o i ∈ C l (5)
Thus, this approach is a supervised normalization scheme where the class labels of each object in the dataset are used to compute the normalization factors.

Estimating the cluster assignments using kernel based clustering

In realistic settings, knowledge of the class labels can not be assumed, whereas an approximate estimate of the number of classes can be guessed more easily by considering the number of abstract classes or concepts that the end use is interested in.

For that reason, we propose to estimate the cluster organization by means of a clustering step performed using the available features at hand. For the sake of simplicity, we considered a raw implementation of the kernel k-means algorithm [START_REF] Shawe | Kernel methods for pattern analysis[END_REF]. However, depending on the specificity of the application scenario of interest, one may consider alternatives approaches. In large scale problems highly efficient approaches based on heuristics such as the ones used considered for community detection [START_REF] Vd | Fast unfolding of communities in large networks[END_REF] can be also considered. Spectral clustering approaches can also be applied for enhanced clustering accuracy [START_REF] Ng | On spectral clustering: Analysis and an algorithm[END_REF].

A qualitative analysis of the proposed approach can be taken by considering Figure 1. It depicts the distribution of distances between a given object and the others as vertical density histograms. The distributions of the raw distance matrix are not centered. Objects with low centered distribution are potential hubs, and object with high centered distribution are potential orphans. Normalizing using LS drastically changed the distributions, imposing a hard threshold for small distances. On contrary, the proposed approach preserves more diversity while minimizing the spread of the distributions.

EXPERIMENTS

In this section, we quantitatively compare the LS approach to the proposed scheme in order to give answers to the following questions:

1. Shall the normalizations be performed iteratively? 2. What is the gain of considering the cluster organization, be it known or estimated, when performing a local normalization?

Different acronyms for the methods under evaluation are used. The i prefix stands for the iterative LS version. For adaptive versions, the neighborhood size can be assumed as a prior (LS p ) or estimated via clustering (LS e ). In the case of clustering, the considered clustering is the one that achieved the lowest average within-cluster distance over 50 runs of the kernel k-means with random initialization. Unless otherwise stated, the number of clusters is set according to the number of classes, e.g. it is considered as a prior.

For each normalization method, the method is either run once or iterated until convergence. The number of iterations is limited to 100, though convergence is achieved in less than 20 iterations in most cases. For the LS method, the neighborhood size K is set to 10.

Evaluation Datasets

A wide range of feature sets taken from three datasets of music and speech were considered (see Table 1).

The Cal500 dataset1 comprises 502 songs. Among the five kernels considered in this study, three are computed from the audio and are supposed to reflect the timbre, rhythm and the harmony. The last two are respectively computed from social tags and the results of web search. More details can be found in [START_REF] Barrington | Combining feature kernels for semantic music retrieval[END_REF].

The Magnatagatune dataset2 comprises 5393 songs which have been organized into 229 clusters according to genre annotations given by listeners. The distance metric considered in this study was obtained by computing the pair-wise similarity between the songs using a state of the art content based approach. More details can be found in [START_REF] Lagrange | Adaptive Nnormalization for Enhancing Music Similarity[END_REF].

The Timit dataset is an acoustic phonetic speech corpus widely used in the speaker recognition community. In this study, we consider the sub corpus composed by Rob Tibshirani 3 , that is made of 5 phonemes spoken by 50 different males speakers. The distance metric considered is a linear kernel of 4509 log periodograms, each representing 30 ms of speech.

For gaining statistical significance and speeding-up computation, each of those feature sets is randomly sampled to build 100 subsets of 500 randomly picked objects. The various normalization methods are applied to the resulting pairwise distance matrices of size 500 by 500 and the results are evaluated using the metrics described in the following section.

Evaluation Metrics

Retrieval of objects within a database that share properties with a given query is perhaps the simplest way of evaluating the effectiveness of a distance measure. In this paper, we consider the Mean Average Precision (MAP) as a measure of accuracy. The MAP is routinely employed in a wide variety of tasks in the information retrieval community [START_REF] Manning | Introduction to information retrieval[END_REF].

As stated before, for a good accuracy, hubs and orphans shall be minimized. To account more precisely for such behaviors, we consider the so-called R-precision, which measures the ratio of the number of relevant documents to the number of retrieved documents, when all relevant documents have been retrieved (i.e. precision at recall equal to one). In that respect, it account well for such unwanted behaviors. Hubs are irrelevantly close neighbors that will therefore decrease the R-precision. Orphans are never close to any items. This will aversely decrease the R-precision.

Results

Cluster awareness

As expected, and as presented in Table 2, when the cluster information is known as a prior, the effectiveness of the normalization is high. This MAP gain decreases when considering the cluster information given by the clustering. Roughly, the accuracy gain of the methods based on the estimated cluster information is approximately half way in between the gains obtained by the constant setting and prior knowledge. Concerning the R-precision, the cluster information is highly beneficial, be it given as a prior or estimated. This lead us to conclude that even if the cluster knowledge is not perfect, it is highly beneficial for better reducing hubs and orphans.

Iterative vs. non iterative normalization

For the Cal500 and Magnatagatune datasets, the use of the iterative version does not provide any gain (see Table 2). On the Timit dataset, the use of the iterative version is positive when taking into account the cluster structure of the data. Table 2. Average MAP (a) and R-precision (b) for several databases before (Ref) and after non-iterative and iterative normalizations.

CONCLUSION

A new contextual scaling approach has been introduced and tested over three datasets issued from the music and speech areas. Experiments showed that the proposed approach reduces unwanted phenomena like hubs and orphans, which results in an accuracy improvement when retrieving objects from a dataset. Future work will focus on experimenting the proposed approach on datasets of different kind and geometry as well as evaluating the robustness of the approach while considering an imperfect prior knowledge of the number of clusters.

Fig. 1 .

 1 Fig.1. Distribution of distances between an object and the remaining objects as vertical density histograms (dark means high density) for a given distance matrix, unprocessed (left), processed with iterative LS (middle) or with the proposed approach (right).

(

Table 1 .

 1 Synthetic overview of the different kernels considered. The cluster size is expressed in terms of average (first value) and standard deviation (second value).

	Name	Size Nb Clus. Size Clus. Kernels
	Cal500	502	20	25 (10)	6
	Magna. 5393	229	24 (20)	1
	Timit	4509	5	902 (192)	1

http://cosmal.ucsd.edu/cal/projects/AnnRet/

http://tagatune.org/Magnatagatune.html

http://www-stat-class.stanford.edu/ ˜tibs/ ElemStatLearn/data.html

This work has been supported by the "Agence Nationale de la Recherche" (French National Funding Agency) in the scope of the JCJC project HOULE and "Fundac ¸ão para a Ciência e Tecnologia" (Portuguese National funds) in the scope of the project ref. PTDC/EIA-CCO/111050/2009.


Christophe Hurez
email: christophe.hurez@developpementdurable.gouv.fr

Cyprien Richer

Does the city's pulse beat at the same rate for men and women? Gender time-geography

Keywords: mobility, gender time-geography, Household Travel Surveys (HTS), schedule mobilité, espace-temps des genres, Enquête Ménage Déplacement

Since the mid-70s, Household Travel Surveys (HTS) in France have been a major source of knowledge of the mobility of inhabitants within a territory. Since 2010, an "Urban Pulse" tool, developed by CETE de Lyon, has offered new perspectives for the use of travel survey data. Like the work based on gender time-geography, the tool enables an accurate understanding of the daily schedules of each individual within a territory, and focuses not only on trips, but also on what happens between two trips: who is where? For what type of activity? Thus, this paper focuses on gender-based spatio-temporal analyses of daily mobility in urban areas of the Rhône-Alpes region. What are the patterns / specificities in the spatial and temporal location of men and women in the cities of Lyon, Grenoble and Saint-Etienne? The "Urban Pulse" tool offers a new perspective on the diversity of urban areas, in the true sense of the term. Finally, these analyses highlight public policy issues that are raised when gender-based mobility is taken into account.

Résumé

Depuis le milieu des années 70 en France, les Enquêtes Ménages Déplacements (EMD) constituent une source importante de connaissance des pratiques de mobilités des habitants d'un territoire. En 2010, l'outil « pulsations urbaines » développé au CETE de Lyon, offre des perspectives nouvelles d'exploitations des données des EMD. A l'image des travaux issus de la time-geography, l'outil offre la possibilité d'appréhender finement les emplois du temps de chaque individu d'un territoire et de ne pas s'intéresser qu'aux seuls déplacements, mais aussi à ce qui se passe entre deux déplacements : Qui est où ? Pour faire quelle activité ? Ainsi, cette contribution porte sur l'analyse spatio-temporelle de la mobilité quotidienne par genre dans le cas des métropoles rhônes-alpines. Quelles sont les régularités/singularités dans la localisation spatiale et temporelle des femmes par rapport à celle des hommes dans les agglomérations de Lyon, Grenoble et Saint-Etienne ? L'outil "pulsation urbaine" propose ainsi, un nouveau regard sur la mixité, au sens propre, des territoires urbains. Au final, ces analyses mettent en évidence les enjeux de politiques publiques que pose la prise en compte des approches de mobilité par le genre.

Observing the pace of life of urban men and women

Society evolves, leading to changes in the pace of life of each citizen. Travel behaviour is more or less shaped by factors such as population ageing, reduced work time, family composition, transport costs etc. Public policymakers need to take into account the reality of the paces of life in order to make informed planning decisions within a territory. The "pulsations" that regulate the daily tempo of the urban frenzy, are, among other things, the reflection of the person's occupational status (employee, student, retiree…), family situation (single or in a couple, with or without children…) but also gender.

Gender has proved to be a major factor explaining travel behaviour. The significant differences between men and women are particularly pronounced when it comes to commuting between home and work. Women's commutes are generally shorter than men's (Madden 1981, Hanson and[START_REF] Hanson | Gender, class, and space[END_REF]McLafferty and Preston, 1991;[START_REF] Lee | Determinants of Commuting Time and Distance for Seoul Residents: The Impact of Family Status on the Commuting of Women[END_REF] and closer to home [START_REF] Carron | Genre et mobilité : quelles différences au sein des couples ? Analyse du microrecensement transport 2005[END_REF]. This is particularly true for suburban households, where women have strong local anchoring, which contrasts with longer commutes of men, who tend to work further from home [START_REF] Cailly | La diversité des modes d'habiter des espaces périurbains dans les villes intermédiaires : différenciations sociales, démographiques et de genre R. Dodier[END_REF]. The cross-analysis of consistencies/specificities in men's and women's behaviour helps to understand how the city moves.

Beyond the single issue of access to employment, we propose to go further into men's and women's pace of daily travel, by analysing their activities during the day. We have chosen to relate this analysis to "timegeography" research work. This approach, developed by the Swedish geographer Torsten [START_REF] Hägerstrand | What about people in regional science[END_REF], provides an analysis of the interactions between temporal and spatial constraints and experiences of individuals during their daily activities. This theory is based on a representation of the accessible space for an individual's activities at a given time of day, the potential access to urban resources and facilities and the individual's personal constraints, [START_REF] Chardonnel | La Time-Geography: les individus dans le temps et dans l'espace[END_REF]. Other contributions [START_REF] Bondi | On the contours of public space : a tale of three women[END_REF][START_REF] Scholten | Re-reading time-geography from a gender perspective: examples from gendered mobility[END_REF], show that time-geography provides a useful set of analytical tools which work successfully with the theory of social sciences, such as gender studies: "time-geography" shares the feminist interest in the quotidian paths traced by people, and again like feminism, links such paths, by thinking about constraints, to the larger structures of society" [START_REF] Rose | Feminism and geography: the limits of geographical knowledge[END_REF]. It therefore seems pertinent to observe daily travel behaviour differences between men and women, using time-geography principles mentioned in recent work [START_REF] Kwan | Affecting geospatial technologies: toward a feminist politics of emotion[END_REF][START_REF] Mcquoid | Bringing emotions to time geography: the case of mobilities of poverty[END_REF]Scholten, Friberg, Sanden, 2012). This article therefore focuses on spatial-temporal analyses of daily travel in urban areas according to gender. What are the major temporal and spatial differences of men's and women' daily trips? The aim of this analysis is to identify common factors and differences in men's and women's daily programmes, and then to identify their spatial distribution throughout the city. The analysis is based on a travel-pulse modelling tool, which draws on data from household travel surveys. Since 2010, the Urban Pulse tool, which has been developed by CETE de Lyon, has helped provide a detailed understanding of the daily schedule of individuals in a given territory. It also enables us to go one step further and provides an analysis of what happens between two trips. In other words, the analysis allows us to know who is present in the city, where, at what time and for which activity. It is a spatial and temporal analysis, also known as "urban pulse", which provides a visualization tool for observing the evolution of a population present in the city. This spatial and temporal analysis consists in identifying the schedule and the location of each interviewe, based on HTS (Household Travel Survey) data.

The raw material of the urban pulse tool is provided by the data from household travel surveys (HTS), carried out in French cities. The data from these surveys provides a picture of trips made by the interviewees on the day before the interview (all kinds of trips for all reasons). The survey therefore provides a reliable description of the travel behaviour of the inhabitants of a given area. Interviewees must accurately describe their travel behaviour, so as to provide representative information of daily mobility. With a sampling rate of 1 to 2%, we know the exact schedule and gender of the interviewees over 5 years old (declarative information). With over 150 HTS interviews, conducted in French cities since 1976, it is an important source of mobility information and highlights differences based on multiple criteria, such as gender.

The geographic areas concerned are the metropolitan areas of the Rhone-Alps region: the cities of Lyon, Grenoble and Saint-Etienne, which have recent HTS data2. There are two main arguments to justify the choice of these urban areas: the first arises from the need to compare these neighbouring, but different cities: Lyon, capital of the Rhone-Alpes region, is a European metropolis; Grenoble is a dynamic regional centre, focused on research and innovation; while Saint-Etienne, which has a population equivalent to Grenoble, is marked by an industrial past and has more disadvantaged populations in comparison with the two other cities. The second reason consists in mitigating local specificities . By comparing the three cities' data, we can identify consistencies and local specificities. Given the contrasted nature of the cities' population, we can easily determine the importance of gender in daily travel behaviour analysis. Could it be used occasionally or systematically to understand the city's pace? This analysis is carried out in three stages. First, it is important to present the main social demographic data of the analysed territories. This information should be put into perspective with the knowledge of men's and women's travel behaviour at the national level. Once that is done, we can apply the urban pulse tool to examine the similarities and differences in men's and women's schedules in three Rhone-Alpes urban areas. Finally, the analysis of daily activities is completed with a spatial dimension that provides a more detailed view of the daily processes of "feminization" or "masculinization" of the three urban areas, depending on the time of the day. Can we identify a city of men and a city of women? Finally, the "urban pulse" tool provides a new look into the diversity of urban territories. These analyses highlight public policy issues that could take gender into account in their approach to mobility.

Activity and mobility according to gender: situation in the Rhone-Alpes metropolitan area

Main occupation by gender: a lower rate of activity for women

The last household travel survey showed that there are generally few differences between Lyon, Grenoble and Saint-Etienne when it comes to occupation: about 40% of the population works (full-time or part-time), 25% is retired and 25% is made up of students, apprentices or school pupils. Only Saint-Etienne differs slightly from Lyon and Grenoble with a lower rate of workers and a stronger rate of retirees, unemployed and women remaining at home. In the three cities studied, the differences between mens' and womens' occupation rates are similar. The share of active men is higher than that of women, but the contrast is especially marked in terms of the type of employment: full-time workers are mostly men (in Lyon 44% for men, 30% for women), whilst parttime workers are mostly women (in Lyon 3% for men, 11% for women). In addition, those declaring that they stay at home are only women, reaching 12% in Saint-Etienne. The other main occupations are relatively balanced even though there are slightly more male students, apprentices, or school pupils and more women who are retired. These contrasts are homogeneous between Lyon, Grenoble and Saint-Etienne, which tends to prove that gender differences are little dependent on local contexts.

Daily travel behaviour: women are as mobile as men but less motorized

Mobility, described as the number of trips per day and per person, is quite similar between men and women in all three cities: around 3.65 in Lyon, 3.9 in Grenoble and 3.8 in Saint-Etienne. Women are slightly more mobile than men in Grenoble and slightly less so in Saint-Etienne. The differences between men and women are more visible if we observe mobility based on the main occupation. Women working part-time are those who on average make the most trips in a given day of the week (4.88 for the Grenoble area). They are substantially more active than men (4.44 for the Grenoble area) while overall, an inhabitant of the Grenoble area makes 3.9 trips per day on average. In the "students" and "retiree" categories, men appear to be slightly more mobile.

In terms of modal share, men figure as the largest users of private cars (in the Lyon area 52% for men, 46% for women), while women are more inclined to walk (29% for men, 36% for women). Public transport users are mostly females, while cyclists and motorised two-wheelers are mostly men. The three urban areas have similar trends although the volumes of each mode vary: in Saint-Etienne, the use of the car is higher while the share of public transport is higher in Grenoble and in Lyon. The modal share for cyclists is also higher in Grenoble.

These observations are consistent with national trends that reflect increasing use of the car for commuting (almost 41% in 1973 and a little more than 72% in 2007). According to the national HTS, more men than women travel to work by car, although women are starting to catch up [START_REF] Roux | Transition de la motorisation en France au vingtième siècle[END_REF]. Women, who on average live closer to their workplace, use more public transport and walk more in comparison to men. Motorized two-wheelers are used marginally by women [START_REF] Roux | Transition de la motorisation en France au vingtième siècle[END_REF]. The same observation can be made with commuting data from INSEE (French national statistics institute): whatever the French region, fewer employed women than men leave their hometown to get to their workplace [START_REF] Houillon | Les différences hommes -femmes dans les déplacements domicile-travail : le cas du Nord-Pas-de-Calais[END_REF]. However, a more specific analysis of the Lyon HTS [START_REF] Certu | La mobilité quotidienne des femmes. Différentes ? Durable ?[END_REF] or the Savoie metropolitan area HTS (CETE de Lyon & Métropole Savoie, 2010) have shown that differences in the use of transport modes is not significantly linked to gender or to professional activity.

The difference between men and women in modal share is mainly linked to a smaller number of driving licences among women, whatever their age. In total, in the Grenoble area, 23% of women of driving age do not have a licence, compared to 10% of men. Analysis by age group reveals two categories for which licence possession is lower: over 65 years old and under 24 years old, where more than 35% of women do not have the opportunity to drive a car. Even if this difference between men and women is gradually decreasing, and the number of women with a driving licence is on the increase3, the contrast is still an explanatory factor of mobility differences. In summary, we can say than women travel as much as men (sometimes more: part-time workers) but differently: more by foot or by public transport and less often by car, which is explained by a lower driving licence rate.

Daily activities: a deeper analysis of differences highlighted by the " urban pulse"tool

The analysis of daily activities offers a more accurate reading of the pace of life for men and women. On their way from home (or on their way back home), activities conducted by women mainly concern purchases (16%), drop-offs or pick-ups (14%) and work (13%). When men leave their home, it is directly to go to work (19%) or to school (14%). Women tend to drop off or pick up others and take care of purchases.

Other studies provide a deeper insight into the differences between men's and women's daily activities. In particular a daily schedule survey conducted by INSEE in 2009-2010 shows that, in the "private" sphere, there remain major differences between the sexes when it comes to the management of daily activities linked to the family, leisure and children. Although today women are catching up with men in terms of driving licence rates, differences still exist in the use of modes of transport4 or the use of their time.

To go further than a simple cumulative estimate of activities and trips, it is interesting to use the "urban pulse" tool to differentiate daily behaviour in terms of time and space. The analysis of the urban pace of life provides an insight into the activities of the residents of the three urban areas, throughout the day. Unlike the 2010 INSEE "schedule survey", the "urban pulse" tool, based on HTS data, does not provide precise knowledge of the activities undertaken within the home. However, they help provide a more spatial vision than the national survey, even if it remains on major types of activities within a personal schedule.

Time distribution of men and women: who does what?

Time spent per activity: differences between active males and females

To refine the programme of activities throughout a day, we calculated the time spent per activity. Thanks to HTS data, we know that Mrs X left her home at 8:00am to arrive at her workplace at 8:20am, etc. We can deduce that, between 4:00am and 8:00am she was at her home, that she was travelling between 8:00am and 8:20am and that from 8:20am she was at work, etc. Nine categories of daily activities were cross-analysed with the main occupation, retaining only the people who travelled at least once during a day. For example, according to the Lyon HTS conducted in 2006, a woman working full-time spends 6h32 at work and 46 minutes travelling in her day.

The following table presents only an excerpt of the analysis of this data, which provides a deeper insight into the differences between men's and women's daily schedules. First, we observe that both men and women spend most of their time at home, about 16 hours a day on average. However, working women spend more time at home than working men (30 minutes to 1hour 20 minutes difference), equivalent to the students/pupils and retirees. In Saint-Etienne, women spend on average 30 minutes more at home than their counterparts in Lyon or Grenoble. This is probably due to the nature of the population, since the Saint-Etienne area has proportionately more retired women and women who stay at home than the two other urban areas.

Figure 1 The time spent at work, about 6 hours for full-time workers and 4 hours for part-time workers, is practically equivalent for men and women but situations may vary: a man working full time will tend to work longer hours than women (especially in the Lyon area where men remain 40 minutes more at work than women). On the other hand, women part-time workers spend either the same or significantly more time at work than men part-time workers: in Grenoble they spend 1 hour more at work than men. There is less contrast in the time spent in studies for students/pupils (about 6 hours), with a slightly longer time for males than females.

In the three urban areas, the time spent on purchases is systematically more significant for women when they work, but equivalent to students/school pupils and retirees. The same observation can be made for the time spent on drop-offs and pick-ups, with women working full-time or part-time spending twice as much time on this activity than men, whereas the difference does not appear for the other categories. On the other hand, women spend less time on leisure activities than men. The difference between men and woman is especially marked for leisure activities for students/ pupils and part-time workers. For example, a female part-time worker in the Grenoble area spends on average 15 minutes per day on leisure activities, compared to 24 minutes for men in the same situation.

The time spent travelling is generally less for women. Once again, this difference concerns the employed while there are fewer contrasts for other categories. We can assume that men, who are more motorized, spend more time travelling because they work further away from home. The study showed that, for women, juggling domestic obligations, work and other daily activities creates a need for their workplace to be near home [START_REF] Nelson | Female Labor Supply Characteristics and the Suburbanization of Low-Wage Office Work[END_REF]. Finally, the time spent outside the geographic area of investigation is also significantly less for women who work. An employed man spends 30 minutes to 1 hour more outside the investigation area than women. The opposite is true for students/pupils where it is women who spend more time outside the investigation area than their male counterparts. It can be noted that in Saint-Etienne, active men working full-time spend more than 2 hours per day outside the perimeter of the HTS. That is twice the time spent by their counterparts in Grenoble or Lyon and probably a sign of a more difficult access to local employment. Thus, for a broadly equivalent time spent at work, a woman spends more time at home. The active woman whether a full-time or part-time worker spends more time on purchases and drop-offs/pick-ups than an active man and less time on leisure activities and travelling. On the other hand, men are more likely to travel outside the HTS investigation area, generally to attain more qualified jobs. Working years coincide with the period in family life when one raises children. Women still tend to take care of the daily management of the family. The distribution of the daily activities of women and men confirm that even when they work, it is women who manage the activities or the tasks of the household. Spare time for part-time workers tends to be used to look after children in the case of women and for leisure activities in the case of the men5.

Daily activities: a more intense programme for women who work

It is possible to refine the analysis of the time spent on daily activities by offering a two-dimensional reading. On a graph, we crossed the rate of presence of men or women with one of the 9 categories of activities within daily schedules. The form of the graph highlights the share of men and women that carry out a given activity. The students/pupils and retiree categories present few gender differences in the schedule. For students/pupils, we can note a similar share between men and women. The peak in travelling at around 8:00am is very pronounced with male or female students/pupils, while presence at home is rather similar: at least 13% of men, at least 15% of women. For retirees, the pace of life of men and women is also rather similar. Once at retirement age, the pace of life of couples tends to resynchronise. Thus, men's and women's schedules are relatively similar for categories that do not have children or no longer look after children. On the other hand, among the employed, contrasts appear in the sequence of daily activities that we have sought to analyse more deeply. Reading: at 7:00am, 90% of women are at home, 4% will not leave their home while the remaining 86% will conduct (or have already conducted) at least one activity during the day.

The first differentiating criterion between employed men and women concerns time spent at home. We already found that on the whole, women spend 1hour more at home than men. We can find this trend in the sequence of daily activities, as at any given time of the day at least 20% of full-time women workers are at home, compared to 16% of men. The same finding is made for the lunch break of the employed, where women are more numerous at home: 38% of women compared to 31% of men. These rates of presence at home are close to average within the Lyon and Grenoble areas, while they are systematically higher for the inhabitants of the Saint-Etienne area.

Outside the home, accompaniment (picks ups or drop offs to the nanny, to nursery, to school...), are more frequent for women and tend to be concentrated around 4 school time slots: 8:30am, 11:30am, 1:30pm and 4:30pm. Similarly, purchases are clearly visible among women from 10am onwards, but are mainly found late afternoon, between 5 pm and 7 pm. Leisure activities mainly take place at the end of the day and are more marked for men. Other activities (administrative tasks, looking for a job, eating outside the home, visits...) are generally concentrated during the lunch break and the evening for men, while they are more evenly spread throughout the day among women. The explanation for this phenomenon relates back to the nature of the activities that fall within the category referred to as "others" and which we can assume are different for men and for women. Men are more likely to spend their lunch breaks outside the home, which explains the concentration of activities in the "others" category during this period. Women tend to conduct these other activities (administrative tasks for example...) in the morning and during the afternoon. The distribution of these activities in a day tends to confirm that the chores of women (e.g. picking up children from school and meal preparation) are more numerous and more sensitive to time constraints than those undertaken by men (e.g. DIY activities) (Mac Donald et al, 2005).

The sequence of the "work" activity presents the same form for men and women. Presence at work is therefore approximately the same with one difference: time of arrival at work, which is earlier for men. In the Grenoble area, 32% of men working full-time are at work at 8:00am, compared to 22% of women. Women make up for this later start at work during their lunch break: at 1:00pm, about 45% of men remain in their workplace, compared to 48% of women. We can equally note that the "outside" category, which generally corresponds to a professional activity outside the investigation area, varies from 4 to 8% for men (implying that at least 4% of men are outside the investigation area all day) and from 2 to 4% for women, with a peak in the middle of the day. Finally, trips are much more marked for men, and are primarily made earlier in the day during peak hours and during the lunchtime period. For women, the time spent travelling is quite similar to men, although trips are spread more throughout the day. Indeed, they visibly travel more in off peak periods.

The main piece of information on daily schedules provided by the graphs concerns the overall duration of men's and women's daily activities. For this, we can observe the period of the day at which less than 90% of the employed are at their home (in others words, the time that begin to leave the home and the time at which they are almost all returned). On average, for men, this period spreads from 5:45am to 11:10pm and for women from 6:45am to 10:15pm. In all the urban areas analysed, the duration is shorter for the women. The overall period during which women conduct their activities outside the home is at least 2 hours less than that that of men! In others words, women carry out as many, or even more activities, but within a shorter period of time! 4. Spatial distribution between men and women: who is where?

4.1. Location throughout the day: are some areas more feminine than others?

Territorial analyses based on urban or peri-urban residence, show that travel behaviour remains relatively homogeneous6. Peri-urban residents use their cars more and travel further, but the daily activities of households in cities and peri-urban areas is quite similar. One of the explanations concerns the double territorial status of the household; in other words, the travel behaviour differences between men and women level out spatial urban/periurban residential differences. It remains to be understood how this "double status " of men and women is translated from a spatial point view? In addition to temporal differences in the daily activities of the men and women, are there also differences in spatial presence within territories (and not only from a residential point of view)? At a given time of day, do territories "have a gender" to resume the expression of [START_REF] Bard | Le genre des territoires. Féminin, masculin, neutre[END_REF]?

Today, urban planning strategies are essentially based on analyses of the resident population in a city. The "urban pulse" tool allows an observation of the population that is physically present at a given time and shows if between two periods of one day, certain areas have a stronger female presence than others, or on the contrary if some areas have a stronger masculine presence. Thanks to HTS information, we know that Miss X left place A at 8:00am and arrived at place B at 8:20am, etc. We can deduce that between 4:00am and 8:00am she was at place A, that between 8:00am and 8:20am she was travelling and that from 8:20am she was at place B, etc. The analysis proposes to observe the share of women present per sector at two moments of a given day. The comparison is made between 4:00am, time at which the great majority of inhabitants are still at their home and 10:30am, time at which most daily activities have begun (school, work, purchases,...). If we observe the densities of inhabitants at 4:00am and the densities present later in the morning, the gender of the territories obeys a daily rhythm. Certain areas that have a stronger masculine presence at night have a stronger feminine presence in the morning and vice-versa. We can identify if a district or a town is «feminized» (this implies than the ratio of women present has increased) or if it is «masculinized » (this means that the ratio of women present decreased). Overall, we can note common trends for the three urban areas studied: the densest central areas tend to become more feminized while the suburbs see the share of men grow. As confirmed by INSEE data, the nature of employment in each geographic area seems to explain why an area becomes feminized or masculinized. However, although jobs have an impact on the travel behaviour of the population, this is not the only reason for the daily movements of men and women. Indeed, the location of shops and other facilities, especially those related to children, (nurseries schools,...) can also account for the masculinization or feminization of certain areas.

«Masculinization» or «féminization» of a city: towards a typology of urban areas

In addition to identifying general trends, we can conduct a deeper analysis by identifying the intensity of daily movements: does the area become more feminized due to the arrival of more women or due to the exodus of men?

An analysis of the spatial nature of men's and women's movements in the Lyon urban area, shows that the areas near the city centre feminize or masculinize due to an increase in population in favour of one gender or the other. These areas provide a large number of jobs and are characterized by contrasting economic activities. In certain cases, men and the women literally switch areas: some come whilst others leave. For example, the eastern part of Lyon (an area with hospitals) is marked by an arrival of women and a loss of men, while in the suburban towns of Chassieu or St-Fons (with numerous industrial jobs) the opposite occurs. Suburban areas, which are not very attractive in terms of job offers, essentially explain the difference between the departures of men and the departures of women. The northern and southern suburbs of Lyon are faced with a greater departure of women than men, while in the eastern and western suburbs there is a more significant departure of men. This tendency can also be found in the urban area of Saint-Etienne where the sectors to the east near the towns of Rive-de-Gier and Saint-Chamond are feminized mainly due to the departure of more men than women; men leaving their home to work in Lyon area. The pace of daily activities and the travel behaviour of women raise have an impact on the household's place of residence. Central locations appear to be important to women, due to their varied activities. The best compromise, taking into account the different types of activity within households would be to live in both dense and mixed environments, with all types of services easily reachable for each individual [START_REF] Carron | Genre et mobilité : quelles différences au sein des couples ? Analyse du microrecensement transport 2005[END_REF]. Central and more "women friendly" locations would help women to juggle both their private and professional life and facilitate daily routines (Butler and Hammett, 1994). On the contrary, living in suburban areas makes daily activities more difficult, especially for women, and will often explain the need for a part-time job, more frequent in these territories [START_REF] Carron | Genre et mobilité : quelles différences au sein des couples ? Analyse du microrecensement transport 2005[END_REF]. The work identified the risk of "spatial entrapment" of women in suburban areas [START_REF] Nelson | Female Labor Supply Characteristics and the Suburbanization of Low-Wage Office Work[END_REF][START_REF] England | Suburban Pink Collar Ghettos: The Spatial Entrapment of Women?[END_REF]: women are willing to accept lower-paid jobs near their home in order facilitate their work-home balance.

Conclusion: a gender time-geography

This article aims to provide a deeper insight into the spatial-temporal dynamics of the daily mobility of men and women through an innovative "urban pulse", tool developed by the CETE de Lyon. Modelling of the daily pace of life in urban areas in the Rhone-Alpes region (Lyon, Grenoble and Saint-Etienne), provides more precise knowledge of the differences in the behaviour of men and women.

The analysis first shows that there are differences in the pace of life of men and women for the employed, but not for students and retirees. We can question if the differences observed between employed men and women are related to the presence or not of a child as the period of employment corresponds to the period in life during which one raises children. It would therefore be useful to conduct further investigations for the employed category of the population, by integrating the composition of the household: couples with or without children, single parent families, single employees.... This analysis also shows that the location of men and women in time and space is a reflection of a territory's characteristics. It is closely linked to the nature and the location of economic activities, but undoubtedly also to the availability of facilities and services. Public decision-makers must therefore bear in mind that men and women do not have the same activities and that their geographic dispersal is different. Facilities and services must be adapted to the different requirements of men and women and take into account whether territories are more feminine or more masculine.

In particular, This work provides a gender "time-geography" which may be characterized by certain clichés: the daily schedule of active women is shorter than that of active men, with more time-related constraints and is therefore differently paced. Travel distances are shorter and less dependent on the car while destinations tend to be closer to the city centre than for men, due to the type of jobs and other facilities. The space-time prism of men and women drawn by this analysis indicates that daily behaviour is still significantly different.

-

  Source: the standard CERTU household travel survey of the Saint-Etienne area realized in 2010 (350 000 inhabitants). To avoid overloading the text, we use shorter references to data sources: «HTS Lyon 2006», «HTS Grenoble 2010» et «HTS St-Etienne 2010».

Figure 3 -

 3 Figure 3-Diagram of the daily share of activities for women/men working full-time in the Lyon, Grenoble and Saint-Etienne urban areas (source: standard HTS, Certu, Cete Lyon)

Figure 4 -

 4 Figure 4-« Feminization » or « Masculinization » of the Lyon, Saint-Etienne and Grenoble urban areas (source: standard HTS Certu, Cete Lyon)

Figure 5 -

 5 Figure 5-« Feminization » or « Masculinization » within the Lyon urban area. (source: standard HTS Certu, Cete Lyon)

Figure 6 -

 6 Figure 6-Simplification of space -time behaviour of men and women (CETE Nord-Picardie)

  -Average time spent per activity by the inhabitants of Greater Lyon who travelled (source: standard HTS Certu, Cete de Lyon )

	Greater Lyon 2006	Full-time workers		Part-time workers
		Women	Men	Diff. women-	Women	Men	Diff. women-
				men			men
	1-Home	14h 57	13h 46	+ 71 min	17h 06	16h 13	+ 53 min
	2-Work	6h 32	7h 12	-40 min	4h 09	4h 11	-2 min
	3-Study	0h 01	0h 00	+ 1 min	0h 00	0h 05	-5 min
	4-Purchases	0h 20	0h 12	+ 8 min	0h 28	0h 13	+ 15 min
	5-Drop-offs or pick-	0h 09	0h 05	+ 4 min	0h 11	0h 03	+ 8 min
	ups
	6-Leisure	0h 14	0h 15	-1 min	0h 15	0h 19	-4 min
	7-Others	0h 35	0h 35	0	0h 41	0h 58	-17 min
	8-Travelling	0h 46	0h 55	-9 min	0h 46	1h 01	-15 min
	9-Outside	0h 22	0h 56	-34 min	0h19	0h 54	-35 min
	investigation area

  Figure 2-Average time spent on activities by the inhabitants of the Lyon, Grenoble and Saint-Etienne urban areas who travelled (source: standard HTS Certu, Cete de Lyon )

	Time spent Home	Work	Purchases Drop-offs-	Leisure	Others	Travelling Outside
					pick ups.				investigation
									area
	Female full-	15 h	6 h	18 min	9 min	14 min	38 min	44 min	31 min
	time workers
	Female	17 h	4 h	26 min	12 min	15 min	42 min	46 min	19 min
	part-time
	workers
	Difference in	1 h less for	= / more	10 min less	5 min	10 min more	=	15 min more	45 min more
	comparison	men	time for	for men	less for men	for men		for men	for men
	with men		male full-
			time
			workers;
			time is less
			for male
			part-time
			workers

Unless otherwise stated all data used in this article are : Source: the standard CERTU household travel survey of the Lyon metropolitan area conducted in 2006 in Greater Lyon (1 100 000 inhabitants) ; -Source: the standard CERTU household travel survey of the greater Grenoble region conducted in 2010 (370 000 inhabitants) ;

Although one woman out of three did not have a driving licence in France in 1974, 76% of women had a driving licence in the first years following 2000(INRETS-DEST, 2001).[START_REF]La motorisation des ménages continue de s'accroître au prix d'un vieillissement du parc automobile[END_REF] shows from the national transportation survey (ENTD) that 76% of women over 55 years old possessed a license, compared to 64% in 1994 and

47% in 1982. This catching up phenomenon is also reflected in the frequency of car use, since 80% of women with a license drove regularly (every week) in 2008, compared to 77% in 1994 (+3 points) 4 Some authors suggest discrimination in terms of car access within the household[START_REF] Paulo | Une mesure des inégalités de mobilité et d'accès au volant[END_REF]

The daily schedule survey conducted by INSEE in 2010 tends to confirm this, since employed men spend 2h06 every day on household activities compared to 3h27 for women. In contrast, men spend 3h28 on leisure activities, compared to 2h48 for women.

Refer to the thesis by Clotilde Minster (IFSTTAR) "Mobility analysis of inhabitants of rural locations as a contribution to comprehension of the demographic revival and sustainability of these spaces"

Acknowledgements

The authors wish to thank CERTU and IFSTTAR who financed the analysis presented in this document, as well as Jingzhu WANG, a geomarketing masters student at Lyon3 University, who conducted work for the CETE Lyon on the urban pulse men of women in the cities of Lyon, Grenoble and Saint-Etienne.