Vincent Lostanlen
email: vincent.lostanlen@nyu.edu

Grégoire Lafay
email: lafaygregoire@gmail.com

Joakim Andén
email: janden@flatironinstitute.org

• Mathieu

Mathieu Lagrange
email: mathieu.lagrange@cnrs.fr

Relevance-based Quantization of Scattering Features for Unsupervised Mining of Environmental Audio

Keywords: unsupervised learning, data mining, acoustic signal processing, wavelet transforms, audio databases, content-based retrieval, nearest neighbor searches, acoustic sensors, environmental sensors

The emerging field of computational acoustic monitoring aims at retrieving high-level information from acoustic scenes recorded by some network of sensors. These networks gather large amounts of data requiring analysis. To decide which parts to inspect further, we need tools that automatically mine the data, identifying recurring patterns and isolated events. This requires a similarity measure for acoustic scenes that does not impose strong assumptions on the data.

The state of the art in audio similarity measurement is the "bag-of-frames" approach, which models a recording using summary statistics of short-term audio descriptors, such as mel-frequency cepstral coefficients (MFCCs). They successfully characterise static scenes with little variability in auditory content, but cannot accurately capture scenes with a few salient events superimposed over static background. To overcome this issue, we propose a two-scale representation which describes a recording using clusters of scattering coefficients. The scattering coefficients capture short-scale structure, while the cluster model captures longer time scales, allowing for more accurate characterization of sparse events. Evaluation within the acoustic scene similarity framework demonstrates the interest of the proposed approach.

Introduction

The amount of audio data recorded from our sonic environment has grown considerably over the past decades. In order to measure the effect of human activity and climate change on animal biodiversity [START_REF] Sueur | Ecoacoustics: the ecological investigation and interpretation of environmental sound[END_REF], researchers have recently undertaken a massive deployment of acoustic sensors throughout the world [START_REF] Warren | Urban bioacoustics: It's not just noise[END_REF][START_REF] Ness | The Orchive: Data mining a massive bioacoustic archive[END_REF][START_REF] Stowell | Large-scale analysis of frequency modulation in birdsong databases[END_REF]. In addition, recent work has explored acoustic monitoring for characterization of human pleasantness in urban areas [START_REF] Guyot | Urban sound environment quality through a physical and perceptive classification of sound sources: A cross-cultural study[END_REF][START_REF] Ricciardi | Sound quality indicators for urban places in Paris cross-validated by Milan data[END_REF], as well as the prediction of annoyance due to traffic [START_REF] Gloaguen | Estimating traffic noise levels using acoustic monitoring: a preliminary study[END_REF]. Since they bear a strong societal impact and raise many scientific challenges, we believe that these applications are of considerable interest for signal processing community.

An important problem is that manually analysing the recorded data to identify the quantities of interest is very costly. Some sort of pre-screening is therefore required to reduce the need for human expert listening and annotation. To this aim, the most straightforward approach is to specify a closed set of sound classes, such as sounds classes expected to appear near the acoustic sensors. Computational models are then trained for these classes which are used to automatically annotate recordings [START_REF] Zhang | Classifying and ranking audio clips to support bird species richness surveys[END_REF]. A given time interval (e.g. a single day) is then represented by the number of events detected during that interval for each class. This allows the scientist to drastically reduce the amount of information requiring manual processing. However, this approach has two drawbacks. First, it relies on trained models whose prediction on unseen data -i.e. sensors outside of the training set -is prone to errors. Secondly, and more importantly, it is based on prior knowledge and thus cannot be considered for exploratory analysis, in which quantities of interest have yet to be defined.

To identify which parts need human inspection, one needs tools that are able to detect both recurring patterns and sparsely distributed events. Identifying recurring patterns allows the user to focus on certain time points for manual annotation, while detection of more rare structures enables discovery of unforeseen phenomena.

With this aim, we need to design an algorithm for acoustic similarity retrieval, where the audio fragments judged "most similar" to a given query recording must be extracted from some larger dataset. To construct such an algorithm, we are required to represent an audio recording in a way that captures its distinctive qualities. A widespread choice of representation is the bag of frames [START_REF] Aucouturier | The bag-of-frames approach to audio pattern recognition: A sufficient model for urban soundscapes but not for polyphonic music[END_REF], which describes an auditory scene recording using summary statistics of short-time features. Unfortunately, the bag-of-frames approach only captures the average structure of the scene, so the approach often fails when presented with highly dynamic scenes or those characterised by a few distinct sound events sparsely distributed over time. Furthermore, experiments in cognitive psychology [START_REF] Dubois | A cognitive approach to urban soundscapes: Using verbal data to access everyday life auditory categories[END_REF] and cognitive neuroscience [START_REF] Nelken | Processing of complex stimuli and natural scenes in the auditory cortex[END_REF] suggest that human acoustic perception is highly sensitive to such isolated sound events. We believe that the failure to model such distinct events is one of the reasons why the bag-of-frames representation is insufficient [START_REF] Lagrange | The bag-of-frames approach: A not so sufficient model for urban soundscapes[END_REF].

Solving the acoustic similarity retrieval first requires the ability to capture meaningful signal structure at small time scales. This is often achieved using mel-frequency cepstral coefficients (MFCCs). Originally developed for speech processing [START_REF] Davis | Comparison of parametric representations for monosyllabic word recognition in continuously spoken sentences[END_REF], MFCCs have recently found wider use in music information retrieval [START_REF] Logan | Mel frequency cepstral coefficients for music modeling[END_REF] and environmental audio processing [START_REF] Aucouturier | The bag-of-frames approach to audio pattern recognition: A sufficient model for urban soundscapes but not for polyphonic music[END_REF]. A richer representation, the scattering transform, has enjoyed significant success in various audio [START_REF] Andén | Deep scattering spectrum[END_REF] and biomedical [START_REF] Chudáček | Scattering transform for intrapartum fetal heart rate variability fractal analysis: A case study[END_REF] signal classification tasks. Its structure is that of a convolutional neural network [START_REF] Lee | Unsupervised feature learning for audio classification using convolutional deep belief networks[END_REF][START_REF] Lostanlen | Deep convolutional networks in the pitch spiral for music instrument classification[END_REF][START_REF] Aytar | SoundNet: Learning sound representations from unlabeled video[END_REF][START_REF] Arandjelović | Look, Listen and Learn[END_REF], but with fixed filters. Specifically, it alternates convolutions with wavelet filters and pointwise nonlinearities to ensure timeshift invariance and time-warping stability [START_REF] Mallat | Group Invariant Scattering[END_REF].

For our task, one advantage of the scattering transform is that it does not require a training step, allowing for a wider range of applications compared to learned features. Indeed, for data mining of previously unheard datasets, the properties of relevant audio structures remains to be defined, leading to an unsupervised setting.

In this work, we propose a new model for acoustic scenes, where the signal is represented at sub-second scales by scattering transforms, while larger scales are captured by a cluster model. This unsupervised model quantizes the scattering coefficients into a given number of clusters. These clusters are then used to define a set of distances for acoustic similarity retrieval. Evaluating this approach on a scene retrieval task, we obtain significant improvements over traditional bag-of-frames and summary statistics models applied both to MFCCs and scattering coefficients.

Motivations of the proposed approach and a brief review of the state of the art in acoustic scene modeling are given in Section 2. We describe the scattering transform in Section 3, discuss feature post-processing in Section 4 and propose a cluster-based scene description in Section 5. Section 6 describes several experiments for the acoustic scene similarity retrieval task. Results are reported in Section 7.

Background

Caracterization of the similarity between audio recordings be they at the scale of the minute, the hour, the day or larger is of interest for many applications areas involving acoustic monitoring such as urban sound environment analysis and ecoacoustics. In this context, a classical approach is the bag of frames (BoF), first applied to the problem by Aucouturier et al. [START_REF] Aucouturier | The bag-of-frames approach to audio pattern recognition: A sufficient model for urban soundscapes but not for polyphonic music[END_REF]. It models an auditory scene using high-level summary statistics computed from local features, typically implemented by Gaussian mixture models (GMMs) of MFCCs.

It is worth mentionning that this task typically falls into a unsupervised paradigm where no prior knowldge is used to model a given scene. For each scene s, a model is compute M s is computed. The similarity among the scene s 1 and s 2 is computed as the similarity, see Section 6 for further details. The BoF approach is also widely used in a supervised fashion for solving a classification task [START_REF] Stowell | Detection and classification of acoustic scenes and events[END_REF]. In this case, each class of scenes from a given typology, say {park, boulevard, square}, is modeled by a GMM trained on scenes taken from a training set. In order to predict the class of a given scene s, the likelihood each model given the scene are computed. The scene is then labeled park if the likelihood of the GMM trained on park scenes is higher than all other likelihoods.

While BoF has largely been superseded by more sophisticated methods for the task of acoustic scene classification [START_REF] Stowell | Detection and classification of acoustic scenes and events[END_REF], it remains the best-performing model for acoustic scene similarity retrieval. Though, this representation was recently shown to perform comparably to direct averaging of the features for a variety of datasets [START_REF] Lagrange | The bag-of-frames approach: A not so sufficient model for urban soundscapes[END_REF]. This contrasts with the typical morphology of acoustic scenes, a "skeleton of events on a bed of textures," where a few discrete sound events are superimposed upon a stationary acoustic background [START_REF] Nelken | An ear for statistics[END_REF]. Such events are not well-characterised by summarizing short-term features, but are better described by large-scale temporal evolution of auditory scenes. The latter approach should therefore prove more fruitful in measuring auditory scene similarity.

This statement has some support in auditory psychology as well as sound synthesis based on summary statistics [START_REF] Mcdermott | Summary statistics in auditory perception[END_REF]. Studies in the cognitive psychology of urban sound environments have shown that global sound level (perceived or measured) is not sufficient to fully characterise an acoustic scene [START_REF] Guyot | Urban sound environment quality through a physical and perceptive classification of sound sources: A cross-cultural study[END_REF][START_REF] Kang | Urban sound environment[END_REF]. Instead, cognitive processes such as sound environment quality perception [START_REF] Dubois | A cognitive approach to urban soundscapes: Using verbal data to access everyday life auditory categories[END_REF] or loudness judgment [START_REF] Kuwano | Memory of the loudness of sounds in relation to overall impression[END_REF] seem to rely upon higher-level cognitive attributes. These typically include the identities of the sound sources which constitute the scene. It has been shown that, if available, the complete description of the scene in terms of event occurrences is powerful enough to reliably predict high-level cognitive classes. For example, in urban areas the presence of birds is likely to be heard in parks and are therefore strong pleasantness indicators. Consequently, research in sound perception is now strongly focused on the contribution of specific sound sources in the assessment of sound environments [START_REF] Ricciardi | Sound quality indicators for urban places in Paris cross-validated by Milan data[END_REF][START_REF] Lavandier | The contribution of sound source characteristics in the assessment of urban soundscapes[END_REF]. Although the complete set of events occurring within a given auditory stream may not be discernable even to human expects, research has shown that a small set of events (so-called markers) suffice to reliably predict many high-level attributes.

From a cognitive psychology perspective, the consensus is therefore that only a few distinct events are sufficient to describe an auditory scene, in contrast to BoF models which treat each observation separately and do not capture their temporal structure. A method that takes this knowledge into account could therefore have potential for great impact in acoustic scene modeling, given a rich enough representation of these distinct events.

Wavelet scattering

Local invariance to time-shifting and stability to time-warping are necessary when representing acoustic scenes for similarity measurement. The scattering transform is designed to satisfy these properties while retaining high discriminative power. It is computed by applying auditory and modulation wavelet filter banks alternated with complex modulus nonlinearities.

Invariance and stability in audio signals

The notion of invariance to time-shifting plays an essential role in acoustic scene similarity retrieval. Indeed, recordings may be shifted locally in time without affecting similarity to other recordings. To discard this superfluous source of variability, signals are first mapped into a time-shift invariant feature space. These features are then used to calculate similarities. Since the features ensure invariance, it does not have to be learned when constructing the desired similarity measure.

Formally, given a signal x(t), we would like its translation x c (t) = x(t -c) to be mapped to the same feature vector provided that |c| T for some maximum duration T that specifies the extent of the time-shifting invariance. We can also define more complicated transformations by letting c vary with t. In this case, we have x τ (t) = x(t -τ (t)) for some function τ , which performs a time-warping of x(t) to obtain x τ (t). Time-warpings model various changes, such as small variations in pitch, reverberation, and rhythmic organization of events. These make up an important part of intra-class variability among natural sounds, so representations must be robust with respect to such transformations.

The wavelet scattering transform, described below, has both of these desired properties: invariance to time-shifting and stability to time-warping. The stability condition can be formulated as a Lipschitz continuity property, which guarantees that the feature transforms of x(t) and x τ (t) are close together if |τ (t)| is bounded by a small constant [START_REF] Mallat | Group Invariant Scattering[END_REF].

Wavelet scalogram

Our convention for the Fourier transform of a continuous-time signal x(t) is x(ω) = +∞ -∞ x(t) exp(-i2πωt) dt. Let ψ(t) a complex-valued analytic bandpass filter of central frequency ξ 1 and bandwidth ξ 1 /Q 1 , where Q 1 is the quality factor of the filter. A filter bank of wavelets is built by dilating ψ(t) according to a geometric sequence of scales 2 γ1/Q1 , obtaining

ψ γ1 (t) = 2 -γ1/Q1 ψ(2 -γ1/Q1 t). (1)
The variable γ 1 is a scale (an inverse log-frequency) taking integer values between 0 and (J 1 Q 1 -1), where J 1 is the number of octaves spanned by the filter bank. For each γ 1 , the wavelet ψ γ1 (t) has a central frequency of 2 -γ1/Q1 ξ 1 and a bandwidth of 2 -γ1/Q1 ξ 1 /Q 1 resulting in the same quality factor Q 1 as ψ. In the following, we set ξ 1 to 20 kHz, J 1 to 10, and the quality factor Q 1 , which is also the number of wavelets per octave, to 8. This results in the wavelet filters covering the whole range of human hearing, from 20 Hz to 20 kHz. Setting Q 1 = 8 results in filters whose bandwidth approximates an equivalent rectangular bandwidth (ERB) scale [28].

The wavelet transform of an audio signal x(t) is obtained by convolution with all wavelet filters. Applying a pointwise complex modulus the transform yields the wavelet scalogram

x 1 (t, γ 1 ) = |x * ψ γ1 |(t). (2)
The scalogram bears resemblance to the constant-Q transform (CQT), which is derived from the short-term Fourier transform (STFT) by averaging the frequency axis into constant-Q subbands of central frequencies 2 -γ1/Q1 ξ 1 . Indeed, both time-frequency representations are indexed by time t and logfrequency γ 1 . However, contrary to the CQT, the scalogram reaches a better time-frequency localization across the whole frequency range, whereas the temporal resolution of the traditional CQT is fixed by the support of the STFT analyzing window. Therefore, the scalogram has a better temporal localization at high frequencies than the CQT, at the expense of a greater computational cost since the inverse fast Fourier transform routine must be called for each wavelet ψ γ1 in the filter bank. However, this allows us to observe amplitude modulations at fine temporal scales in the scalogram, down to 2Q 1 /ξ 1 for γ 1 = 0, of the order of 1 ms given the aforementioned values of Q 1 and ξ 1 .

To obtain the desired invariance and stability properties, the scalogram is averaged in time using a lowpass filter φ(t) with cut-off frequency 1/T (and approximate duration T ), to get

S 1 x(t, γ 1 ) = x 1 (•, γ 1 ) * φ(t), (3)
which is known as the set of first-order scattering coefficients. They capture the average spectral envelope of x(t) over scales of duration T and where the spectral resolution varying with constant Q. In this way, they are closely related to the mel-frequency spectrogram and related features, such as MFCCs.

Extracting modulations with second-order scattering

In auditory scenes, short-time amplitude modulations may be caused by a variety of rapid mechanical interactions, including collision, friction, turbulent flow, and so on. At longer time-scales, they also account for higher-level attributes of sound, such as prosody in speech or rhythm in music. Although they are discarded while filtering x 1 (t, γ 1 ) into the time-shift invariant representation S 1 x(t, γ 1 ), they can be recovered from x 1 (t, γ 1 ) by a second wavelet transform and another complex modulus. We define second-order wavelets ψ γ2 (t) in the same way as the first-order wavelets, but with parameters ξ 2 , J 2 , and Q 2 . Consequently, they have central frequencies 2 -γ2/Q2 ξ 2 for γ 2 taking values between 0 and (J 2 Q 2 -1). While this abuses notation slightly, the identity of the wavelets should be clear from context. The amplitude modulation spectrum resulting from a wavelet modulus decomposition using these second-order wavelets is then

x 2 (t, γ 1 , γ 2 ) = |x 1 * ψ γ2 |(t, γ 1 ). ( 4
)
In the following, we set ξ 2 to 2.5 kHz, Q 2 to 1, and J 2 to 12. Lastly, the low-pass filter φ(t) is applied to x 2 (t, γ 1 , γ 2 ) to guarantee local invariance to time-shifting, which yields the second-order scattering coefficients

S 2 x(t, γ 1 , γ 2 ) = x 2 (•, γ 1 , γ 2 ) * φ(t). (5)
The scattering transform Sx(t, γ) consists of the concatenation of firstorder coefficients S 1 x(t, γ 1 ) and second-order coefficients S 2 x(t, γ 1 , γ 2 ) into a feature matrix Sx(t, γ), where γ denotes either γ 1 or (γ 1 , γ 2 ). While higherorder scattering coefficients can be calculated, for the purposes of our current work, the first and second order are sufficient. Indeed, higher-order scattering coefficients have been shown to contain reduced energy and are therefore of limited use [START_REF] Waldspurger | Exponential decay of scattering coefficients[END_REF]. Wavelets ψ γ1 (t) and ψ γ2 (t) are designed as fourth-order Gammatone wavelets with one vanishing moment [START_REF] Venkitaraman | Auditorymotivated Gammatone wavelet transform[END_REF], and are shown in Figure 1. In the context of auditory scene analysis, the asymmetric envelopes of Gammatone wavelets are more biologically plausible than the symmetric, Gaussian envelopes of the more widely used Morlet wavelets. Indeed, it allows to reproduce two important psychoacoustic effects in the mammalian cochlea: the asymmetry of temporal masking and the asymmetry of spectral masking [28]. The asymmetry of temporal masking is the fact that a masking noise has to be louder if placed after the onset of a stimulus rather than before. Likewise, because critical bands are skewed towards higher frequencies, a masking tone has to be louder if it is above the stimulus in frequency rather than below. It should also be noted that Gammatone wavelets follow the typical amplitude profile of natural sounds, beginning with a relatively sharp attack and ending with a slower decay. As such, they are similar to filters discovered automatically by unsupervised encoding of natural sounds [START_REF] Smith | Efficient auditory coding[END_REF][START_REF] Sainath | Learning the speech front-end with raw waveform CLDNNs[END_REF]. In addition, Gammatone wavelets have proven to outperform Morlet wavelets on a benchmark of supervised musical instrument classification from scattering coefficients [START_REF] Lostanlen | Convolutional operators in the time-frequency domain[END_REF]. This suggests that, despite being hand-crafted and not learned, Gammatone wavelets provide a sparser time-frequency representation of acoustic scenes compared to other variants. More information can be found in Annex 9.

Feature design

Before constructing models for similarity estimation, it is beneficial to process scattering coefficients to improve invariance, normality, and generalization power. In this section, we review two transformations which achieve these properties: logarithmic compression and standardisation.

Logarithmic compression

Many algorithms in pattern recognition, including nearest neighbor classifiers and support vector machines, tend to work best when all features follow a standard normal distribution across all training instances [START_REF] Hsu | A practical guide to support vector classification[END_REF]. Yet the distribution of the scattering coefficients is skewed towards larger values. We can reduce this skewness by applying a pointwise concave transformation to all coefficients. In particular, we find that the logarithm performs particularly well in this respect. Figure 2 shows the distribution of an arbitrarily chosen scattering coefficient over the DCASE 2013 dataset, before and after logarithmic compression.

[Fig. 2

about here.]

Taking the logarithm of a magnitude spectrum is ubiquitous in audio signal processing. Indeed, it is corroborated by the Weber-Fechner law in psychoacoustics, which states that the sensation of loudness is roughly proportional to the logarithm of the acoustic pressure. We must also recall that the measured amplitude of sound sources often decays polynomially with the distance to the microphone-a source of spurious variability in scene classification. Logarithmic compression linearise this dependency, facilitating the construction of powerful invariants at the classifier stage.

Standardisation

Let Sx(γ, n) be a dataset, where γ and n denote feature and sample indices, respectively. Many algorithms operate better on features which have zero mean and unit variance to avoid mismatch in numeric ranges [START_REF] Hsu | A practical guide to support vector classification[END_REF]. To standardise Sx(γ, n), we subtract the sample mean vector µ[Sx(γ)] from Sx(γ, n) and divide the result by the sample standard deviation vector σ[Sx](γ). The vectors µ[Sx(γ)] and σ[Sx](γ) are estimated from the entire dataset.

Acoustic scene similarity retrieval

As discussed in Section 2, results in sound perception suggest the appropriateness of source-driven representations of auditory scenes for predicting highlevel properties. While this can be addressed in the supervised case using late integration of discriminative classifiers [START_REF] Andén | Deep scattering spectrum[END_REF], this is not directly feasible in the unsupervised case. As the detection of events is still an open problem [START_REF] Stowell | Detection and classification of acoustic scenes and events[END_REF], we consider in this paper a generic quantization scheme in order to identify and represent time intervals of the scene that are coherent, thus likely to be dominated by a given source of interest.

Given a set of d-dimensional feature vectors X u = {x u 1 , . . . , x u L }, extracted from the scene s u , where u = {1, 2, . . . , U }, we would like to partition X u into a set C u = {c u 1 , . . . , c u M } of M clusters. This partition is obtained by minimizing the variance of each cluster and known as a k-means clustering [START_REF] Lloyd | Least squares quantization in PCM[END_REF]. Each scene s u is then described by a set of clusters C u . Note that this quantization approach differs from unsupervised learning schemes such as the ones studied in [START_REF] Bisot | Acoustic scene classification with matrix factorization for unsupervised feature learning[END_REF], where the scene features are projected in a dictionary learned from the entire dataset. Here, with the aim of better balancing the influence of salient sound events and texture-like sounds on the final decision, the similarity between two scenes is computed based on the similarity of their centroids. The similarity between the scene centroids µ u m over the entire dataset, is computed using a radial basis function (RBF) kernel K combined with a local scaling method [START_REF] Zelnik-Manor | Self-tuning spectral clustering[END_REF]:

K uv mn = exp - µ u m -µ v n 2 µ u m -µ u m,q µ v n -µ v n,q . (6)
Here, µ u m,q and µ v n,q are the q th nearest neighbors to the centroids µ u m and µ v n , respectively, and the double bars • denotes the Euclidean norm.

To compute the similarity between two scenes, we consider several centroidbased similarity metrics:

-Relevance-based Quantization closest similarity (RbQ-c): the similarity between two scenes s u and s v is equal to the largest similarity between their centroids max m,n

K uv mn , (7)
-Relevance-based Quantization average similarity (RbQ-a): the similarity between two scenes s u and s v is equal to the average of their centroid similarities 1

M 2 m,n K uv mn (8)
and, -Relevance-based Quantization weighted similarity (RbQ-w ): the similarity between two scenes is computed using a variant of the earth mover's distance applied to the set of centroids each weighted by the number of frames assigned to its cluster.

For RbQ-w, each scene is represented by a signature

p u = {(µ u 1 , w u 1 ), (µ u 2 , w u 2 ), . . . , (µ u M , w u M )},
where each of the M centroids µ u 1 , . . . , µ u M are paired with corresponding weights w u 1 , . . . , w u M . The weight w u m for the mth centroid µ u m is the number of frames belonging to a particular cluster. The similarity between scenes is then given by a cross-bin histogram distance known as the non-normalized earth mover's distance EMD introduced by [START_REF] Pele | A linear time histogram metric for improved SIFT matching[END_REF]. The EMD computes the distance between two histograms by finding the minimal cost for transforming one histogram into the other, where cost is measured by the number of transported histogram counts multiplied by a dissimilarity measure between the histogram bins. Here, that measure is given by 1 -K uv mn .

Experiments

To evaluate the representations introduced in the previous section, we apply it to the acoustic scene similarity retrieval task. Results demonstrate the improved performance of the relevance-based quantization of scattering coefficients compared to baseline methods using summary statistics of MFCCs. The implementations of the presented methods and the experimental protocol are available online.1

Dataset

The experiments in this paper are carried out on the publicly available DCASE 2013 dataset [START_REF] Stowell | Detection and classification of acoustic scenes and events[END_REF]. Although the dataset was constructed for the task of acoustic scene classification, where the goal is to correctly assign the class of a given recording, we can use the same recordings and class labels for the task of acoustic scene similarity retrieval. The dataset consists of two parts, a public and a private subset, each made up of 100 acoustic scene recordings sampled at 44100 Hz and 30 seconds in duration. The dataset is evenly divided into 10 acoustic scene classes: bus, busy street, office, open air market, park, quiet street, restaurant, supermarket, tube, and tube station. The recordings were made by three different recordists at a wide variety of locations in the Greater London area over a period of several months. In order to avoid any correlation between recording conditions and label distribution, all recordings were carried out under moderate weather conditions, at varying times of day and week, and each recordist recorded each scene type. As a result, the dataset enjoys significant intra-class diversity while remaining of manageable size, making it suitable for evaluation of algorithmic design choices [START_REF] Lagrange | The bag-of-frames approach: A not so sufficient model for urban soundscapes[END_REF]. As an illustration, Figure 3 represents the wavelet scalogram of one recording within the DCASE 2013, labeled as park.

[Fig. 3 about here.]

Feature design

We perform our experiments using both scattering coefficients and MFCCs. For the scattering transform, each 30-second scene is described by 128 vectors of dimension 1367 computed with half-overlapping windows φ(t) of duration T = 372 ms, for a total of 24 s. Here we discard 3 seconds from the beginning and end of the scene to avoid boundary artifacts. We also conduct experiments with and without logarithmic compression of the scattering coefficients (see Section 4.1). MFCCs are computed for windows of 50 ms and hops of 25 ms with full frequency range. The standard configuration of 39 coefficients coupled with an average-energy measure performs best in preliminary tests, so we use this in the following. We average the coefficients using 250 ms long non-overlapping windows so that each window represents structures of scales close to that of scattering coefficients.

Evaluation and algorithm

The evaluation is performed on the private part of the DCASE 2013 dataset. As a metric, we use the precision at rank k (p@k). This number is computed by taking a query item and counting the number of items of the same class within the k closest neighbors, and then averaging over all query items. We determine these neighbors using one of the proposed similarity measures RbQc, RbQ-a, or RbQ-w. We compute p@k for k = {1, . . . , 9}, since each class only has 10 items. Note that p@1 is equal to the classification accuracy obtained by the nearest-neighbor classifier in a leave-one-out cross-validation setting.

The RbQ measures are compared to commonly used early integration approach early, which consists in averaging over time the feature set of each scene, resulting in one feature vector per scene. The distance on this average feature vector is then used to determine p@k. For the BoF approach of Aucouturier et al. [START_REF] Aucouturier | The bag-of-frames approach to audio pattern recognition: A sufficient model for urban soundscapes but not for polyphonic music[END_REF], GMMs are estimated for each scene using the expectation-maximization (EM) algorithm [START_REF] Dempster | Maximum Likelihood from Incomplete Data via the EM Algorithm[END_REF][START_REF] Moon | The expectation-maximization algorithm[END_REF]. The similarity between a given pair of scene GMMs is then calculated through Monte Carlo sampling approximation. To ensure convergence of the EM algorithm for the scattering features, we reduce their dimension from 1367 to 30 by projecting the features onto the top 30 principal components of the dataset. the number of Gaussians is optimized for each type of features by grid search in the range [START_REF] Warren | Urban bioacoustics: It's not just noise[END_REF][START_REF] Arandjelović | Look, Listen and Learn[END_REF]. Best p@5 is reached with 8 and 4 Gaussians, respectively for MFCCs and scattering features. Recommended number of Gaussians for MFCCs given in [START_REF] Aucouturier | The bag-of-frames approach to audio pattern recognition: A sufficient model for urban soundscapes but not for polyphonic music[END_REF] is 10.

The scaling parameter q of the RBF kernels (see Eq. 6) is set to 10% of the number of data points to cluster. As the number of Gaussians for the BoF approach, the numbers of clusters M controls the level of abstraction. For each method, unless otherwise stated, the parameter M is set to 8. It thus allows 8 different types of observations to be modeled, which seems reasonable given the duration of the scene (30 seconds). Note that this is the only free parameter in the proposed method. However, except for RbQ-a, the results are not very sensitive to the choice of M , as long as it is large enough to characterize the seen. A numerical demonstration is provided at the end of the next section.

Results

Results for the acoustic scene similarity retrieval task demonstrate that logarithmically compressed scattering features outerform MFCCs. Combining these with the RbQ cluster model, improvements are obtained over traditional BoF and summary statistic measures.

Baselines

As seen in Figure 4, scattering features significantly outperform the baseline MFCCs for both BoF and early integration schemes. This is expected, as the scattering transform extends the MFCCs by including supplementary amplitude modulation information [START_REF] Andén | Deep scattering spectrum[END_REF]. We also note that applying PCA reduction to the scattering transform has little effect for the early integration scheme. In the context of summary statistics, 30 dimensions are sufficient to discriminate between auditory scenes.

Comparing the BoF to early integration, both approaches perform similarly for MFCCs and PCA-reduced scattering features alike. This is in line with previous results on BoF [START_REF] Lagrange | The bag-of-frames approach: A not so sufficient model for urban soundscapes[END_REF], where it is found to perform similarly as similarity retrieval on features averaged over the entire recording.

The early approach being simpler in terms of implementation and runtime complexity, we retain this method as baseline for the remainder of the experiments.

[Fig. 4 about here.]

Logarithmic compression

Figure 5 shows that logarithmic compression of the scattering features is beneficial. For clarity sake, data is shown for the early approach only, but a equivalent gain is achieved for the relevance-based quantization approaches.

[Fig. 5 about here.]

MFCC vs. scattering transform

Irrespective of the rank k considered, best result is achieved for the scattering transform with logarithmic compression using the RbQ-c approach. Overall, log-compressed scattering coefficients systematically outperform MFCCs. This is to be expected since the scattering coefficients capture larger-scale modulations, as opposed to MFCCs which only describe the short-time spectral envelope.

Relevance-based quantization vs. early integration

For the scattering transform, both RbQ-c and RbQ-w outperform early, thus confirming the benefits of using an relevance-based quantization (RbQ) to improve the similarity measures between the scenes. However, it is worth noting that RbQ-a performs comparably to or worse than early, showing that the discriminant information is destroyed by averaging the contributions from all centroids. This result is in line with the findings of [START_REF] Lagrange | The bag-of-frames approach: A not so sufficient model for urban soundscapes[END_REF]. To take advantage of such a representation, we need to select certain representative centroids when comparing quantized objects. The same behavior is observed for MFCCs, with RbQ-c and RbQ-w outperforming early, which is equivalent to the state-of-theart BoF model, as seen previously.

Furthermore, it appears that RbQ-c is better able to characterise the classes compared to RbQ-w. Although not the only way of incorporating the number of frames associated to each centroid, the earth mover's distance is a rather natural of doing so. Its worse performance therefore suggests that including this information may not always be desirable. Indeed, nothing a priori indicates that the discriminant information between two scenes lays within the majority of their frames. On the contrary, two similar environments may share a lot of similar sound sources with only a few sources discriminating between them.

With p@5 as our metric (cf. [START_REF] Aucouturier | The bag-of-frames approach to audio pattern recognition: A sufficient model for urban soundscapes but not for polyphonic music[END_REF] and [START_REF] Lagrange | The bag-of-frames approach: A not so sufficient model for urban soundscapes[END_REF]), we see that replacing MFCCs by the logarithmically compressed scattering transform increases performance from 0.31 to 0.49. In addition, the relevance-based quantization using the closest similarity (RbQ-c) further improves the performance to 0.54 for a global increase of 0.23.

[Fig. 6 about here.]

Sensitivity to number of clusters M

We now study the sensitivity of the precision at rank 5 (p@5) with respect to the number of clusters M . The results are shown in Figure 7.

For a small number of clusters (M = 1 or M = 2), all methods perform worse, since not enough discriminative sound objects are extracted from the recording. Please note that setting M = 1 is equivalent to the early approach as this corresponds a summary statistics model. For M = 4, most methods perform well, since this allows for better characterization of various signal structures in the scenes. As the number of clusters increases, the RbQa method performs worse for both scattering features and MFCCs since any distinct objects are averaged out by clusters representing the background. The RbQ-w and RbQ-c methods do better in this regard, as they are better able to emphasize the clusters that discriminate well between scenes.

Using RbQ-c, therefore, we are not very sensitive to the choice of M , as long as it is large enough to allow for separation of the discriminative sound objects from the background. This motivates our choice of M = 8 for the previous experiments in this section.

[Fig. 7

about here.] 8 Conclusion

This paper presents a new approach for modeling acoustic scenes based on scattering transforms at small scales and cluster-based representations at large scales. Compared to traditional BoF and summary statistics models, this representation allows for the characterization of distinct sound events superimposed on a stationary texture, a concept which has strong grounding in the cognitive psychology literature. To adequately capture such distinct events, we develop a cluster-based model and validate it using experiments on acoustic scene similarity retrieval. For this task, we show significant improvements over the traditional BoF and summary statistics models based on both standard MFCCs and scattering features. These outcomes shall be studied further in future work by considering larger databases and emerging tasks in ecoacoustics [START_REF] Sueur | Ecoacoustics: the ecological investigation and interpretation of environmental sound[END_REF][START_REF] Wimmer | Sampling environmental acoustic recordings to determine bird species richness[END_REF].

filter bank in a discrete-time setting. Then, we relate the bandwidth parameter σ to the choice of a quality factor Q.

Motivation

Time reversal of a real signal x(t) is equivalent to the complex conjugation of its Fourier transform x(ω). As a consequence, the Fourier transform modulus | x(ω)| is not only invariant to translation, but also invariant to time reversal. Yet, although invariance to translation is needed for classification, invariance to time reversal is an undesirable property. A simple way to break invariance to time reversal is to choose as an asymmetric wavelet instead of a Gabor symmetric wavelet.

The complex-valued Gammatone wavelet is a modification of the realvalued Gammatone auditory filter, originated in auditory physiology. The Gammatone auditory filter of dimensionless frequency 1 is defined as a gamma distribution of order N ∈ N * and bandwidth σ modulated by a sine wave, that is, t N -1 exp(-2πσt) cos(2πt).

For a fixed σ, the integer N controls the relative shape of the envelope, becoming less skewed as N increases. Psychoacoustical experiments have shown that, for N = 4, the Gammatone function provides a valid approximation of the basilar membrane response in the mammalian cochlea [START_REF] Flanagan | Models for approximating basilar membrane displacement[END_REF][START_REF] Patterson | Auditory filter shapes derived with noise stimuli[END_REF][START_REF] Lyon | History and future of auditory filter models[END_REF]. In particular, it is asymmetric both in the time domain and in the Fourier domain, which allows to reproduce the asymmetry of temporal masking as well as the asymmetry of spectral masking [28]. It is thus used in computational models for auditory physiology [START_REF] Pressnitzer | Real-time auditory models[END_REF]. However, it does not comply with the Grossman-Morlet admissibility condition, because it has a non-negligible average. In addition, because the Gammatone auditory filter takes real values in the time domain, its Fourier transform satisfies Hermitian symmetry, which implies that it does not belong to the space H 2 of analytic functions. More generally, there are no real-valued functions in H 2 [START_REF] Grossmann | Decomposition of Hardy functions into square integrable wavelets of constant shape[END_REF].

Related work

With the aim of building a pseudo-analytic admissible Gammatone wavelet, [START_REF] Venkitaraman | Auditorymotivated Gammatone wavelet transform[END_REF] have modified the definition of the Gammatone auditory filter, by replacing the real-valued sine wave cos(2πt) by its analytic part exp(2πit) and by taking the first derivative of the gamma distribution, thus ensuring null mean. The definition of the Gammatone wavelet becomes

ψ(t) = 2π(i -σ)t N -1 + (N -1)t N -2 exp(-2πσt) exp(2πit)
in the time domain, and

ψ(ω) = iω × (N -1)! (σ + i(ω -σ)) N
in the Fourier domain. Besides its biological plausibility, the Gammatone wavelet enjoys a near-optimal time-frequency localization with respect to the Heisenberg uncertainty principle. Furthermore, this time-frequency localization tends to optimality as N approaches infinity, because the limit N → +∞ yields a Gabor wavelet [START_REF] Cohen | Time-frequency analysis[END_REF]. Last but not least, the Gammatone wavelet transform of finite order N is causal, as opposed to the Morlet wavelet transform, which makes it better suited to real-time applications. From an evolutionary point of view, it has been argued that the Gammatone reaches a practical compromise between time-frequency localization and causality constraints [START_REF] Venkitaraman | Auditorymotivated Gammatone wavelet transform[END_REF].

Center frequency parameter

In order to preserve energy and allow for perfect reconstruction, the Gammatone wavelet filter bank must satisfy the inequalities

1 -ε ≤ | φ(ω)| + γ | ψ(2 γ ω)| + | ψ(-2 γ ω)| ≤ 1
for all frequencies ω, where ε is a small margin [START_REF] Andén | Deep scattering spectrum[END_REF]. Satisfying the equation above near the Nyquist frequency ω = π can be achieved by placing the logfrequency log 2 ξ of the first (topmost) wavelet in between the log-frequency log 2 (ξ × 2 -1/Q ) of the second wavelet and the log-frequency log 2 (2π -ξ) of the mirror of the first wavelet. We obtain the equation log 2 ξ -log 2 (ξ × 2 -1/Q ) = log 2 (2π -ξ) -log 2 ξ, of which we deduce the identity ξ = 2π 1 + 2 1/Q . For Q = 1, this yields a center frequency of ξ = 2π 3 . For greater values of Q, the center frequency ξ tends towards π.

Bandwidth parameter

The quality factor Q of the Gammatone wavelet is defined as the ratio between the center frequency ξ of the wavelet ψ(ω) and its bandwidth B in the Fourier domain. This bandwidth is given by the difference between the two solutions ω of the following equation:

| ψ(ω)| | ψ(ξ)| = ω ξ × 1 + (ω -ξ) 2 σ 2 -N/2 = r,
where the magnitude cutoff r is most often set to 1 2 . Let ∆ω = ω -ξ. Raising the above equation to the power N/2 yields the following:

1 + ∆ω ω c N/2 = r × 1 + ∆ω 2 α 2 .

3. 4

 4 Gammatone wavelets [Fig. 1 about here.]

Fig. 1

 1 Fig. 1 Gammatone wavelets ψ(t) in the time domain with quality factors (a) Q = 4 and (b) Q = 1. Oscillations (red, blue) are the real and imaginary parts. The envelope (yellow) is the complex modulus.

Fig. 2 FIGURESFig. 3

 23 Fig. 2 Histogram of values taken by the first-order scattering coefficient Sx(γ), corresponding to a central acoustic frequency of 302 Hz, (a) before and (b) after logarithmic compression.

Fig. 4

 4 Fig. 4 Acoustic scene similarity retrieval in the DCASE 2013 private dataset: precisions at rank k (p@k) obtained for several baseline approaches, as a function of the rank k.

Fig. 5

 5 Fig. 5 Acoustic scene similarity retrieval in the DCASE 2013 private dataset: precisions at rank k (p@k) obtained for scattering with or without logarithmic compression, as a function of the rank k.

Fig. 6

 6 Fig. 6 Acoustic scene similarity retrieval in the DCASE 2013 private dataset: precisions at rank k (p@k) obtained for MFCCs and scattering with logarithmic compression.

Fig. 7

 7 Fig. 7 Acoustic scene similarity retrieval in the DCASE 2013 private dataset: precision at rank 5 (p@5) obtained for different methods as a function of the number of clusters M .

https://github.com/mathieulagrange/paperRelevanceBasedSimilarity

Funding

This study is co-funded by the ANR under project reference ANR-16-CE22-0012.

Availability of data and materials

The dataset supporting the conclusions of this article is available in the dcase2013 repository, http://c4dm.eecs.qmul.ac.uk/ sceneseventschallenge/description.html. The software supporting the conclusions of this article is available in -Companion website: https://github.com/mathieulagrange/ paperRelevanceBasedSimilarity -Programming language: Matlab -License: GNU GPL -Any restrictions to use by non-academics: license needed

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

GL and VL carried out the numerical experiments and drafted the manuscript. VL, GL, JA and ML participated in the design of the study and helped to draft the manuscript. All authors read and approved the final manuscript.

Since ∆ω ξ, we may approximate the left-hand side with a first-order Taylor expansion. This leads to a quadratic equation of the variable ∆ω:

The discriminant of the above equation is:

which is a positive number as long as r < 1. The bandwidth B of ψ is given by the difference between the two solutions of the quadratic equation, that is:

Now, let us express the parameter α as a function of some required bandwidth B at some cutoff threshold r. After having raised the above to its square and rearranged the terms, we obtain another quadratic equation, yet of the variable

We multiply the equation by

This leads to defining σ 2 as the unique positive root of the above polynomial:

If the filter bank has to be approximately orthogonal, we typically set B to

We conclude with the following closed form for α:

where

List of Figures


Félix Gontier
email: felix.gontier@ls2n.fr

Pierre Aumond

Mathieu Lagrange

Catherine Lavandier

Jean-François Petiot

Jean-Francois Petiot

Towards perceptual soundscape

Keywords: Soundscape, urban acoustic monitoring, event detection

come   L'archive ouverte pluridisciplinaire

INTRODUCTION

The ongoing urbanization process has led to an increase in sound quality concerns. In urban areas the noise has been linked to several health issues including sleep-related troubles as well as heart disease rates, and is a major cause for city dwellers' annoyance in certain areas. In this context, the 2002/49/CE European directive [START_REF] Ec | Directive 2002/49/ec of the european parliament and of the council of 25 june 2002 relating to the assessment and management of environmental noise[END_REF] requires that large cities maintain noise maps to facilitate the development of noise reducing plans. These noise maps are mainly based on predictive maps generated using propagation and emission acoustic models. The studies are also 1) often limited to traffic and other transportation sources, and 2) no fusions of simulations with physical measurements are used. Furthermore, the models depend on data that may be at times or in certain locations unavailable or incomplete. The advent of the internet of things (IoT) presents an opportunity for the development of large, scalable networks of acoustic sensors [START_REF] Mydlarz | The implementation of low-cost urban acoustic monitoring devices[END_REF][START_REF] Gontier | An efficient audio coding scheme for quantitative and qualitative large scale acoustic monitoring using the sensor grid approach[END_REF]. The "characterization of urban sound environments" (CENSE) project [START_REF] Picault | Characterization of urban sound environments using a comprehensive approach combining open data, measurements, and modeling[END_REF] aims at implementing such a network to produce perceptually motivated noise maps.

The ISO 12913-1 [START_REF]Acoustics -soundscape -part 1: definition and conceptual framework[END_REF] standard gives the following definition of soundscape: "the acoustic environment as perceived and understood and/or experienced by people and/or society, in context". The assessment of subjective descriptors [START_REF] Berglund | On a tool for measuring soundscape quality in urban residential areas[END_REF][START_REF] Brown | Towards standardization in soundscape preference assessment[END_REF][START_REF] Aletta | Soundscape descriptors and a conceptual framework for developing predictive soundscape models[END_REF] such as the liveliness or calmness is thus necessary to evaluate the quality of urban scenes. The relevant attributes describing the appreciation of soundscapes can be mapped in perceptual spaces [START_REF] Axelsson | A principal components model of soundscape perception[END_REF][START_REF] Cain | The development and application of the emotional dimensions of a soundscape[END_REF]. The set of considered attributes is reduced to a few dimensions which are used as a basis for perceptual experiments. Specifically, the dimension of pleasantness is increasingly associated with soundscape quality in recent works [START_REF] Coensel | The quiet rural soundscape and how to characterize it[END_REF][START_REF] Delaitre | Influence of loudness of noise events on perceived sound quality in urban context[END_REF][START_REF] Ricciardi | Sound quality indicators for urban places in paris cross-validated by milan data[END_REF][START_REF] Aumond | Modeling soundscape pleasantness using perceptive assessments and acoustic measurements along paths in urban context[END_REF]. Soundscape perception is highly dependent on the composition of the scene [START_REF] Lavandier | The contribution of sound source characteristics in the assessment of urban soundscapes[END_REF][START_REF] Nilsson | Soundscape quality in suburban green areas and city parks[END_REF]. Indeed, each sound source yields a different perceptual response. For example, soundscape pleasantness is likely to be improved by birdsongs and deteriorated by mechanical noises.

Acoustic monitoring applications typically rely on the measurement of energetic (sound levels, eg. LAeq) and psychoacoustic (eg. Zwicker's loudness N ) indicators. These global quantities describe the overall activity, with percentile values linked to event or background assessment. However they do not differentiate sound sources and are thus not sufficient to a perceptual characterization of soundscapes. Additional information about the taxonomic classification of active sources and their distribution in time is needed. Several sets of relevant indicators have been studied [START_REF] Can | Capturing urban traffic noise dynamics through relevant descriptors[END_REF][START_REF] Can | Comparison of noise indicators in an urban context[END_REF][START_REF] Brocolini | Measurement of acoustic environments for urban soundscapes: choice of homogeneous periods, optimization of durations, and selection of indicators[END_REF] to better account for the specificities of each scene and their source composition.

The use of large-scale sensor networks yields a problematic for the extraction of content-related quantities of interest from important amounts of data. Despite a growing interest in the community, machine learning models -to the best of our knowledge -were not yet specifically targeted to the prediction of source-specific perceptual parameters in complex urban environments. Most event detection applications focus on obtaining a precise annotation of source activity, within usual ranges of tens of milliseconds. The estimation of sound levels involves entirely different models through source separation and regression [START_REF] Gloaguen | Estimating traffic noise levels using acoustic monitoring: a preliminary study[END_REF] and longer time scales.

We believe that the use of machine listening techniques could greatly benefit the automatic assessment of urban soundscape quality using sensor networks. The aim of this paper is to 1) bring some context of soundscape characterization, and 2) report on a perceptual experiment performed in order to study which features shall be brought by automatic event detection systems in order to gather relevant information for the task of characterize perceptual attributes of the soundscape.

SOUNDSCAPE CHARACTERIZATION

Urban soundscape monitoring has only scarcely been studied by the machine listening community [START_REF] Bello | Sound analysis in smart cities[END_REF]. This work aims at contributing to this task by focusing on pleasantness as it is the most recurrent descriptor of urban soundscape quality, though similar studies could be led for other notions such as liveliness.

Several perceptual experiments on the urban soundscape quality have indeed proposed a model of pleasantness from other per- ceptual parameters [START_REF] Nilsson | Acoustic indicators of soundscape quality and noise annoyance in outdoor urban areas[END_REF][START_REF] Axelsson | A principal components model of soundscape perception[END_REF][START_REF] Aumond | Modeling soundscape pleasantness using perceptive assessments and acoustic measurements along paths in urban context[END_REF][START_REF] Ricciardi | Sound quality indicators for urban places in paris cross-validated by milan data[END_REF]. In all cases, a good approximation of pleasantness can be obtained by linear combination of both overall and source-specific parameters evaluated on discrete scales. Global parameters consider the sound scene in its entirety for which the overall loudness is commonly used. The parameters used for the assessment of source-wise contributions include 1) the sound level where each source is considered separately, 2) the emergence or dominance relating to the influence of the source in the global mix, or 3) the time of presence, that is the ratio of time where the source s is heard in a given scene. The notion of time of presence is of particularly interest as it hints at the possibility of automatic prediction through event detection systems. The corresponding model is:

T T T T V B B B T V B Time V B B V T T (
P = aL + s bsTs,p + c ( 1
)
where P is the scene's pleasantness, L is the perceived overall level and Ts,p is the perceived time of presence for source s. These parameters are evaluated on discrete scales through perceptual tests.

The coefficients a, bs and c are usually found via multiple linear regression and thus differ in each study. Furthermore, three principal source categories are usually identified: mechanical, human and nature. Mechanical sounds are mainly composed of traffic and are mostly found to have a negative impact on soundscape pleasantness, whereas nature sources such as bird activity or water sounds have a positive influence and human sounds (voices) can yield mixed effects.

Assuming this perceptual model, the prediction of pleasantness can be assimilated as that of perceived times of presence of sources. Three levels of metrics are thus identified. First, the physical level Figure 1(a) is evaluated on the presence and emergence of the three identified sound sources: traffic (T), voice (V) and birds (B). The second level Figure 1 The transition model between the perceived time of presence per source and pleasantness has already been proposed. However no previous work exists that uses detection models for the estimation of source-specific subjective parameters. The feasibility of assessing source perception from the postulated metrics at the physical level shall be verified as a first step prior to building the full estimation model.

FROM PHYSICAL TO PERCEPTUAL TIME OF PRESENCE OF SOURCES

We thus conduct a perceptual experiment to validate this key step of the estimation procedure. We wish to study the relation between extracted source-dependent physical indicators to their perceptual equivalents, then validate the relevance of the first level of metrics introduced in the previous section.

Perceptual Test

For this test, a set of sound scenes recorded in the 13th district of Paris as part of the GRAFIC project [START_REF] Aumond | Modeling soundscape pleasantness using perceptive assessments and acoustic measurements along paths in urban context[END_REF] is used as reference. Some artificial scenes with equivalent event sequencing are also used for which the acoustic properties of each active source can be computed precisely.

Of the 19 different recording locations, 9 are selected to represent diverse compositional properties: park (P3, P9), quiet street (P5, P11, P13, P17), noisy street (P2, P6) and very noisy street (P16). Corresponding artificial scenes are simulated following the method described in [START_REF] Gloaguen | Creation of a corpus of realistic urban sound scenes with controlled acoustic properties[END_REF]. Simulations are obtained using the sim-Scene software [START_REF] Lafay | A morphological model for simulating acoustic scenes and its application to sound event detection[END_REF]. To do so, the recordings are first annotated by identifying active background and event sources. Background sounds are present throughout the whole scene and are characterized by an absolute level parameter. Conversely, events are localized occurrences that are defined by their onset and duration as well as an event-to-background ratio (EBR). The sound scenes are simulated from these annotations and a database of extracts for isolated sources obtained on freesound.org, see [START_REF] Gloaguen | Creation of a corpus of realistic urban sound scenes with controlled acoustic properties[END_REF] for more details. This ensures that ground truth source-specific presence and sound level can be computed. One minute of audio is extracted for each scene such as no single event overwhelms the rest of the excerpt.

During the test, the order of appearance is as follows: the original recorded scenes from locations P3 and P16 representing quiet and very noisy environments are always presented first to help participants use the full range of the scale during the test. The 9 simulated sounds are then presented in random order to limit order biases over the participants population. For each scene, 14 criteria are evaluated on a 0-10 scale by the subject. These parameters are displayed in French, but translated in English in this paper for the sake of clarity. The first four questions cover global perceptual parameters:

1. Noisy -Quiet: Overall perceived loudness (OL), Source-specific perceived time of presence (scale Never -Continuously) and sound level (scale Very low -Very high) are also evaluated. The considered sources are traffic (T), birds (B), horns and sirens (H), human voice (V) and footsteps (F). The perceived time of presence and level for source s are respectively noted Ts,p and Ls,p in the remainder of this paper.

Participants can only listen to each scene once and must answer all questions before proceeding to the next scene. All subjects used the same hardware desktop configuration, sound card and software, as well as Beyerdynamics DT-990 headphones in a quiet environment. The same output volume on headphones was set by the experimenter for all scenes and participants. The resulting playback sound level ranged from approximately 50 dB to 78 dB over the corpus. 30 subjects took the test in 3 sessions, all reported normal hearing conditions.

Perceptual space

An outlier detection procedure is applied on the 270 resulting assessments (30 subjects, 9 scenes). An assessment is rejected when its distance from the mean is higher than 3 standard deviations at the question level, that is for each parameter of each scene. The results from two participants with more than 10% assessments considered as outliers are removed from the study.

The perceptual space produced by the test is first compared to previous studies in the literature. This is to ensure that relevant conclusions can be made on further analysis. Figure 2 shows the standardized principal component analysis (PCA) of the average values of the four general questions at the scene level (n=9). The two components respectively explain 52.3% and 30.5% of the global variance. It is found that liveliness (L) correlates poorly with calmness (C), while interest (I) is between the two. These results can be compared to previous studies on similar soundscape qualities parameters [START_REF] Axelsson | A principal components model of soundscape perception[END_REF][START_REF] Cain | The development and application of the emotional dimensions of a soundscape[END_REF][START_REF] Jeon | A cross-national comparison in assessment of urban park soundscapes in france, korea, and sweden through laboratory experiments[END_REF], where interest and calmness were established as almost independent. The scale of liveliness was in both cases correlated similarly with the two others. However, just as the principal components space is slightly distorted in [START_REF] Jeon | A cross-national comparison in assessment of urban park soundscapes in france, korea, and sweden through laboratory experiments[END_REF] due to the study being focused on park environments. The correspondence between these results on global perceptual parameters and those of the literature allows us to think that perceptual data on sources are relevant for this study.

Proposed indicators

As discussed in Section 2 several models have been established to assess pleasantness as a function of global and source-specific parameters. The main objective of this work is to link physical indicators to perceptual source-specific parameters to ultimately predict pleasantness from acoustical data without perceptual assessments. Thus, physical indicators are computed from the audio tracks obtained during scene simulation. To evaluate the overall loudness of the scene, three measurements are chosen in accordance to previous studies [START_REF] Coensel | The quiet rural soundscape and how to characterize it[END_REF][START_REF] Ricciardi | Sound quality indicators for urban places in paris cross-validated by milan data[END_REF][START_REF] Aumond | Modeling soundscape pleasantness using perceptive assessments and acoustic measurements along paths in urban context[END_REF]:

• L50: Z-weighted (no weighting over the observed frequency range) sound level exceeded 50% of the time in dB, • LA50: A-weighted sound level exceeded 50% of the time in dBA, • L50 for the 1kHz band only.

Source-specific indicators are also computed: the time of presence and an emergence estimation metric (resp. Ts and Ls for source s), obtained by subtracting the global L90 (Z-weighted level exceeded 90% of the time), found to represent well background activity, to the L10 of each source. Sound levels are computed with the Matlab ITA toolbox [START_REF] Berzborn | The ita-toolbox: an open source matlab toolbox for acoustic measurements and signal processing[END_REF] in the 20 Hz-20 kHz range.

In the considered scenes, background sources are always active. The measurement of time of presence is thus limited to sound events which leads to relatively poor representation of the scene perception. Furthermore, the ground truth indicators are computed for each source separately and do not consider the potential impact of other sources active at the same time. Two additional indicators are thus designed regarding these considerations.

The first proposed indicator Ts(α) is a time of presence metric relying on the emergence of each sound source relative to the others. Sound levels (dB) are computed for audio frames of 125 ms. This duration is approximately that of the shortest event found during annotation and corresponds to the "fast" measurements used in acoustical monitoring applications. The emergence, i.e. difference ∆s(t) of sound levels between the studied source (Ls(t)) and the background constituted of all others (L b (t)) is computed. The source is then considered present on a given time frame if the emergence is greater than a threshold value α. A time of presence measurement is obtained by averaging over time:

Ts(α) = 1 Nt N t t=1 1 ∆s(t)>α (2)
where Nt is the total number of 125 ms analysis frames in the scene. The optimal threshold α is optimized via grid search to maximize the resulting correlation with the 45 average perceptual time of presence assessments. An optimal value of α = -31dB for the considered corpus is found. As the sound levels of tested scenes range from 50 dB to 78 dB (cf. Section 3.1), only sources with very low sound level on the whole spectrum are considered not heard. However, the masking of a sound by another does not depend only on the emergence over the whole frequency spectrum. The spectral distribution is important, the level comparison shall thus be made around the characteristic frequency components of a source. A second indicator Ts(α, β), based on a spectral decomposition is thus proposed. Third-octave bands sound levels are computed on 125 ms frames and the emergence of a source compared to the background is defined as Similarly to the first metric Ts(α, β) then relies on simple thresholds applied on the emergence, first in frequency then in time. Its expression is as follows:

∆s(t, f ) = Ls(t, f ) -L b (t, f ) (3)
Ts(α, β) = 1 Nt N t t=1 1 N f f =1 ∆s(t, f )1 ∆s(t,f )>α N f f =1 1 ∆s(t,f )>α > β (4)
where N f is the number of third-octave bands. Here the emergence threshold α is applied to each frequency band of the signal at a given time frame. To determine if the source is heard in the frame a second threshold β is then used on the mean emergence of the source on emergent bands. Again, optimal values for parameters αopt = -6dB and βopt = -5dB are found via grid search on the experiment corpus as no other subset of scenes with both physical and perceptual data is available. This set of values is more plausible physically, as it indicates that a source is considered heard if its sound level is at most 5 dB lower than that of other sources overlapping in time and frequency. Table 1 shows the Pearson's correlation coefficients between the computed indicators and assessed parameters at the sound scene level (n=9). The three globally computed sound levels L50, LA50 and L 50,1kHz represent well the perceived overall loudness of the scene and can be used directly for pleasantness prediction. Ground truth emergences also correlate with the evaluated sound level parameters for all sources but traffic. The perceived time of presence is however represented poorly by its corresponding ground truth estimation in common background sources: traffic, birds and human voices. Traffic, specifically, is almost always present throughout a scene in real life conditions. Its ground truth activity thus does not vary significantly across the considered corpus, although high variations in perceptual assessments indicate that it may not be heard at all time. The two proposed indicators successfully account for this effect for background sources while yielding similar correlations for horns and footsteps. Furthermore, these parameters are more discriminative for traffic and birds. This confirms the need of an emergence-based time of presence indicator to successfully represent heard sources in the scene's mix.

For all sources the perceived time of presence and sound level are highly correlated (r > 0.8, p < 0.01). This is not the case for the corresponding acoustic indicators, indicating information redundancy between these two quantities at the perceptual level. As a result one of the two quantities is often omitted in proposed pleasantness models.

CONCLUSION

A pilot experiment was performed to assess the relevance of predicting perceptual parameters from acoustic indicators in simulated scenes for soundscape quality assessment. The ground truth time of presence of sources is found not sufficient to fully characterize soundscape perception. Some sources can be active but not heard in the mix, especially background sounds such as traffic. This illustrates the need to design a masking model-based metric to determine each source's perceptual importance in complex soundscapes. The proposed indicator Ts(α, β), while relying on a basic emergence model due to the small amount of available data, can be directly linked to source-specific perceptual quantities. Predicting the average pleasantness of a soundscape can thus be achieved by estimating the source activity and emergence indicators proposed in Section 2.

Precision requirements of the postulated physical metrics are also obtained. 125 ms or longer time scales used for the computation of all indicators in the presented experiment allow the design of perceptually relevant indicators. A binary masking model is shown in this study to improve parameter prediction. The estimation of source-wise emergence as a classification process (e.g. 4 classes from Not heard at all to Dominant) as opposed to continuous regression is thus sufficient for the application needs.

Future work will 1) consider a refined perceptual experiment with a richer soundscape corpus in order to achieve a stronger validation and model design including comparison with state-of-the-art masking models and 2) formulate a complete experimental protocol dedicated to the soundscape characterization task.

Figure 1 :

 1 Figure 1: The three suggested levels of metrics to predict soundscape pleasantness. (a) Traffic (T), voice (V) and bird (B) events are detected and their sound level roughly estimated. (b) The perceptual time of presence for each source is computed on one-minute frames, resulting in a pleasantness value (c).

  (b) is the perceived time of presence for each source represented as a scalar in the 0-1 range. The third level Figure 1(c) is the estimate of pleasantness, also represented as a 0-1 scalar. Both the perceptual levels of metrics are only relevant on longer time scales, about one minute being a usual value in existing experiments.

2 .

 2 Boring, uninteresting -Stimulating, interesting: Interest (I), 3. Inert, amorphous -Lively, eventful: Liveliness (L), 4. Agitated, chaotic -Calm, peaceful: Calmness (C).

Figure 2 :

 2 Figure 2: Principal component analysis (first two components) of the four general perceptual parameters at the scene level (n=9). The observed space is distorted although comparable that of previous works in the literature.

Table 1 :

 1 Pearson correlation coefficients between perceptual parameters and physical indicators at the scene level (n=9). *: p < 0.05, **: p < 0.01, non-significant correlations (p > 0.05) are noted NS.

	Phys./Perc.	OL	I	L	C	LT,p	TT,p	LB,p	TB,p	LH,p	TH,p	LV,p	TV,p	LF,p	TF,p
	L50,1kHz	0.93**	NS	NS	-0.92**	0.75*	0.7*	NS	NS	NS	NS	NS	NS	NS	NS
	L50	0.98**	NS	0.73*	-0.97**	0.72*	NS	NS	NS	NS	NS	NS	NS	NS	NS
	LA50	0.96**	NS	0.73*	-0.94**	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS
	TT	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS
	LT	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS
	TB	NS	0.67*	NS	NS	0.71*	0.75*	NS	NS	NS	NS	NS	NS	NS	NS
	LB	NS	0.93**	NS	NS	-0.84** -0.83** 0.91** 0.82**	NS	NS	NS	NS	NS	NS
	TH	NS	NS	NS	NS	NS	NS	NS	NS	NS	0.84**	NS	NS	NS	NS
	LH	NS	NS	NS	NS	NS	NS	NS	NS	0.98**	0.78*	NS	NS	NS	NS
	TV	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS
	LV	NS	NS	0.81**	NS	NS	NS	NS	NS	NS	NS	0.84** 0.88**	NS	NS
	TF	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	0.9**	0.68*
	LF	NS	NS	-0.72*	NS	NS	NS	NS	NS	NS	NS	-0.69*	-0.78* 0.92**	NS
	TT (α)	NS	-0.81**	NS	NS	0.90**	0.94**	NS	NS	NS	NS	NS	NS	NS	NS
	TT (α, β)	NS	-0.80**	NS	NS	0.88**	0.92**	NS	NS	NS	NS	NS	NS	NS	NS
	TB(α)	NS	0.88**	NS	NS	NS	NS	0.95** 0.97**	NS	NS	NS	NS	NS	NS
	TB(α, β)	NS	0.88**	NS	NS	NS	NS	0.95** 0.97**	NS	NS	NS	NS	NS	NS
	TH (α)	NS	NS	NS	NS	NS	NS	NS	NS	NS	0.83**	NS	NS	NS	NS
	TH (α, β)	NS	NS	NS	NS	NS	NS	NS	NS	0.73*	0.88**	NS	NS	NS	NS
	TV (α)	NS	NS	0.82**	NS	NS	NS	NS	NS	NS	NS	0.79*	0.83**	NS	NS
	TV (α, β)	NS	NS	0.82**	NS	NS	NS	NS	NS	NS	NS	0.75*	0.79*	NS	NS
	TF (α)	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	-0.71* 0.87**	NS
	TF (α, β)	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	NS	0.90** 0.70*