One-Class SVMs Challenges in Audio Detection and Classiﬁcation Applications

Support vector machines (SVMs) have gained great attention and have been used extensively and successfully in the ﬁeld of sounds (events) recognition. However, the extension of SVMs to real-world signal processing applications is still an ongoing research topic. Our work consists of illustrating the potential of SVMs on recognizing impulsive audio signals belonging to a complex real-world dataset. We propose to apply optimized one-class support vector machines (1-SVMs) to tackle both sound detection and classiﬁcation tasks in the sound recognition process. First, we propose an e ﬃ cient and accurate approach for detecting events in a continuous audio stream. The proposed unsupervised sound detection method which does not require any pretrained models is based on the use of the exponential family model and 1-SVMs to approximate the generalized likelihood ratio. Then, we apply novel discriminative algorithms based on 1-SVMs with new dissimilarity measure in order to address a supervised sound-classiﬁcation task. We compare the novel sound detection and classiﬁcation methods with other popular approaches. The remarkable sound recognition results achieved in our experiments illustrate the potential of these methods and indicate that 1-SVMs are well suited for event-recognition tasks.


INTRODUCTION
Kernel-based algorithms have been recently developed in the machine learning community, where they were first introduced in the support vector machine (SVM) algorithm.There is now an extensive literature on SVM [1] and the family of kernel-based algorithms [2].The attractiveness of such algorithms is due to their elegant treatment of nonlinear problems and their efficiency in high-dimensional problems.They have allowed considerable progress in machine learning and they are now being successfully applied to many problems.
Kernel methods, which are considered one of the most successful branches of machine learning, allow applying linear algorithms with well-founded properties such as generalization ability, to nonlinear real-life problems.They have been applied in several domains.Some of them are direct application of the standard SVM algorithm for sound detection or estimation and others incorporate prior knowledge into the learning process, either using virtual training sam-ples or by constructing a relevant kernel for the given problem.The applications include speech and audio processing (speech recognition [3], speaker identification [4], extraction of audio features [5], and audio signal segmentation [6]), image processing [7], and text categorization [8].This list is not exhaustive but shows the diversity of problems that can be treated by kernel methods.
It is clear that many problems arising in signal processing are of statistical nature and require automatic data analysis methods.Moreover, there are lots of nonlinearities so that linear methods are not always applicable.In signal processing field, a key method for handling sequential data is the efficient computation of pairwise similarity between sequences.Similarity measures can be seen as an abstraction between particular structure of data and learning theory.One of the most successful similarity measures thoroughly studied in recent years is the kernel function [9].Various kernels have been developed for sequential data in many challenging domains [8,[10][11][12].This is primarily due to new exciting application areas like sound recognition [6,[13][14][15].
In this field, data are often represented by sequences of varying length.These are some reasons that make kernel methods particularly suited for signal processing applications.Another aspect is the amount of available data and the dimensionality.One needs methods that can use little data and avoid the curse of dimensionality.
Support vector machines (SVMs) have been shown to provide better performance than more traditional techniques in many signal processing problems, thanks to their ability to generalize especially when the number of learning data is small, to their adaptability to various learning problems by changing kernel functions, and to their global optimal solution.For SVMs, few parameters need to be tuned, the optimization problem to be solved does not have numerical difficulties-mostly because it is convex.Moreover, their generalization ability is easy to control through the parameter ν, which admits a simple interpretation in terms of the number of outliers [2].
This paper focuses on the new challenges of SVMs on sound detection and classification tasks in an audio recognition system.In general, the purpose of sound (event) recognition is to understand whether a particular sound belongs to a certain class.This is a sound recognition problem, similar to voice, speaker, or speech recognition.Sound recognition systems can be partitioned into two main modules.First, a sound detection stage isolates relevant sound segments from the background by detecting abrupt changes in the audio stream.Then, a classifier tries to assign the detected sound to a category.
Generally, the classical event detection methods are based on the energy calculation [16].In recent years, some new methods based on a model selection criterion have attracted more attention especially in the speech community and has been applied in many statistical sound detection methods especially for speaker change detection [17][18][19][20].On the other hand, the sounds classifiers are often based on statistical models.Examples of such classifiers include Gaussian mixture models (GMMs) [21], hidden Markov models (HMMs) [22], and neural networks (NNs) [23].In many previous works, it was shown that most of the used paradigms for sound recognition tasks perform very well on closed-loop tests, but performance degrades significantly on open-loop tests.As an attempt to overcome this drawback, the use of adaptive systems that provide better discrimination capabilities often results in overparameterized models which are also prone to overfitting.All these problems can be attributed simply to the fact that most systems do not generalize well.
In this paper, we focus on the specific task of event detection and classification using the one-class SVMs (1-SVMs).1-SVM distinguishes one class of data from the rest of the feature space given only a positive data set.Based on a strong mathematical foundation, 1-SVM draws a nonlinear boundary of the positive data set in the feature space using a parameter to control the noise in the training data and another one to control the smoothness of the boundary.1-SVMs have proved extremely powerful in some previous audio applications [6,15,24].
The sound detection and classification steps are represented in Figure 1.Only the colored blocks in the sound recognition process will be addressed in this paper.For the event detection task, the proposed approach which does not require any pretrained models (unsupervised learning) is based on the use of the exponential family model and 1-SVMs to approximate the generalized likelihood ratio, thus increasing robustness and allowing detecting events close to each others.For the sound classification task, the proposed approach presented has several original aspects, the most prominent being the use of several 1-SVMs to perform multiple class classification and the use of a sophisticated dissimilarity measure.In this paper, we will demonstrate that the 1-SVM methodology creates reliable classifiers (i.e., classifiers with very good generalization performance) more easy to implement and tune than the common methods, while having a reasonable computation cost.
The remainder of this paper is organized as follows.Section 2 gives an overview of the 1-SVM-based learning theory.We discuss the proposed 1-SVMs-based algorithms and approaches to sound detection in Section 3 and to sound classification in Section 4. Experimental results and discussions are provided in Section 5. Section 6 concludes the paper with a summary.

THE ONE-CLASS SVMs
The One-class approach [2] has been successfully applied to various problems [10,15,[25][26][27].To denote a one-class classification task, a large number of different terms have been used in the literature.The term single-class classification originates from Moya [28], but also outlier detection [29], novelty detection [6,23] or concept learning [30] are used.The different terms originate from the different applications to which one-class classification can be applied.Obviously, its first application is outlier detection examples, to detect uncharacteristic objects from a dataset, which do not resemble the bulk of the dataset in some way.These outliers in the data can be caused by errors in the measurement of feature values, resulting in an exceptionally large or small feature value in comparison with other training objects.In general, trained classifiers only provide reliable estimates for input objects resembling the training set.
1-SVM distinguishes one class of data from the rest of the feature space given only a positive data set (also known as target data set) and never sees the outlier data.Instead, it must estimate the boundary that separates those two classes based only on data which lie on one side of it.The problem therefore is to define this boundary in order to minimize misclassifications by using a parameter to control the noise in the training data and another one to control the smoothness of the boundary.
The aim of 1-SVMs is to use the training dataset X = {x 1 , . . ., x m } in R d so as to learn a function f X : R d → R such that most of the data in X belong to the set R X = {x ∈ R d with f X (x) ≥ 0} while the volume of R X is minimal.This problem is termed minimum volume set (MVS) estimation [31], and we see that membership of x to R X indicates whether this datum is overall similar to X, or not.Thus, by learning regions R Xi for each class of sound (i = 1, . . ., N), we learn N membership functions f Xi .Given the f Xi 's, the  ) .The 1-SVM algorithm defines a hyperplane with equation W = { ∈ H s.t.w, H − ρ = 0}, orthogonal to w. Black dots represent the set of mapped data, that is, k(x j , •), i = 1, . . ., m.For RBF kernels, which depend only on x − x , k(x, x ) is constant, and the mapped data points thus lie on a hypersphere.In this case, finding the smallest sphere enclosing the data is equivalent to maximizing the margin of separation from the origin.assignment of a datum x to a class is performed as detailed in Section 4.1.
1-SVMs solve MVS estimation in the following way.First, a so-called kernel function k(•, and it is assumed to be positive definite [2].Here, we assume a Gaussian RBF kernel such that k(x, x , where • denotes the Euclidean norm in R d .This kernel induces a so-called feature space denoted by H via the mapping φ : R d → H defined by φ(x) k(x, •), where H is shown to be reproducing kernel Hilbert space (RKHS) of functions, with dot product denoted by •, • H . (We stress on the difference between the feature space, which is a (possibly infinite dimensional) space of functions, and the space of feature vectors, which is R d .Though confusion between these two spaces is possible, we stick to these names as they are widely used in the literature.)The reproducing kernel property implies that φ(x), φ(x ) which makes the evaluation of k(x, x ) a linear operation in H , whereas it is a nonlinear operation in R d .In the case of the Gaussian RBF kernel, we see that φ(x) 2 H φ(x), φ(x) H = k(x, x) = 1, thus all the mapped data are located on the hypersphere with radius one, centered onto the origin of H denoted by S (o,R=1) (Figure 2).The 1-SVM approach proceeds in feature space by determining the hyperplane W that separates most of the data from the hypersphere origin, while being as far as possible from it.Since in H the image by φ of R X is included in the segment of hypersphere bounded by W , this indeed implements MVS estimation [31].In practice, let , then its parameters w(•) and ρ result from the optimization problem min w,ξ,ρ subject to (for j = 1, . . ., m) where ν tunes the fraction of data that are allowed to be on the wrong side of W (these are the outliers and they do not belong to R X ) and ξ j 's are so-called slack variables.It can be shown [2] that a solution of (1)-( 2) is such that where the α j 's verify the dual optimization problem Finally, the decision function is and ρ is computed by using f X (x j ) = 0 for those x j 's in X that are located onto the boundary, that is, those that verify both α j / = 0 and α j / = 1/νm.An important remark is that the solution is sparse, that is, most of the α i 's are zero (they correspond to the x j 's which are inside the region R X , and they verify f X (x) > 0).
As plotted in Figure 2, the MVS in H may also be estimated by finding the minimum volume hypersphere that encloses most of the data (support vector data description (SVDD) [26,32]), but this approach is equivalent to the hyperplane one in the case of an RBF kernel.
In order to adjust the kernel for optimal results, the parameter σ can be tuned to control the amount of smoothing, that is, large values of σ lead to flat decision boundaries.Also, ν is an upper bound on the fraction of outliers in the dataset [2].

APPLICATION OF 1-SVMs TO SOUND DETECTION
The detection of an event (called the useful sound) is very important because if an event is lost during the first step of the system, it is lost forever.On the other hand, if there are too many false alarms, the sound recognition system is saturated.Therefore, the performance of the detection algorithm is very important for the entire recognition system.There are many techniques previously used for sound detection with a very simple functional principle (a threshold on energy), or with a statistical model [16,33].Very simple methods based either on the variance or on the median filtering of the signal energy have been used in many previous works.In [34][35][36], three algorithms were used: one based on the cross-correlation of two successive windows, a second one based on the error of energy prediction, and a third one based on the wavelet filtering.Another method widely used in the speech community is based on model selection using Bayesian information criterion (BIC) [20].Our objective is to develop a new robust unsupervised sound detection technique based on a new 1-SVMs-based algorithm that uses the exponential family model.In this section, we begin by giving a brief description of some previous works with a special emphasis on the BIC detection method.

Previous works
Sound detection is the first step of every sound analysis system and is necessary to extract the significant sounds before initiating the classification step.Here, we present four classical event detection algorithms: cross-correlation, energy prediction, wavelet filtering, and BIC.The first three methods are widely used for impulsive sound detection [34] and they are based on the energy calculation and use a threshold which must be settled empirically.In recent years, the last method, BIC, has attracted more attention in the speech community and has been applied in many statistical sound detection methods especially for speaker change detection [17][18][19][20].The Bayesian information criterion is a model selection criterion that was first proposed by [37] and widely used in the statistical literature.
The cross-correlation detection method is based on the measure of similarity between two successive signal windows in order to find abrupt changes of the signal.The algorithm calculates the cross-correlation function between two windows and keeps the maximum value.Finally, a threshold on this signal is applied (if the signal is under the threshold, an event detection is generated) [34].The energy prediction-based detection method computes the signal energy on N sample windows.The next value of the energy is predicted based on the L previous values (L = prediction length) using the spline interpolation method [36].Finally, a threshold is settled on the prediction error (the absolute difference between the real value and the predicted value).The wavelet filtering-based sound detection method [35] uses wavelets such as Daubechies to compute DWT [38].The sound detection algorithm computes the energy of the high-order wavelet coefficients which are the most significant coefficients for short and impulsive signals.
The sound detection is achieved by applying a threshold on the sum of energies.
The change detection via BIC algorithm [20] is based on the measure of the ΔBIC [39] value between two adjacent windows.The sequence containing these two windows is modeled as one or two multivariate Gaussian distributions.The null hypothesis that the entire sequence is drawn from a single distribution is compared to the hypothesis that there is a segment boundary between the two windows which means that the two windows are modeled by two different distributions.When the BIC difference between the two models is positive (ΔBIC > 0), we place a segment boundary between the two windows, and then begin searching again to the right of this boundary [18].

Sound detection using 1-class SVM and exponential family
In most commonly used model selection sound detection techniques such as the BIC detection method previously described, the basic problem may be viewed as a two-class classification.Where the objective is to determine whether N consecutive audio frames constitute a single homogeneous window W or two different windows W 1 and W 2 .In order to detect if an abrupt change occurred at the ith frame within a window of N frames, two models are built.One which represents the entire window by a Gaussian characterized by μ (mean), Σ (variance); a second which represents the window up to the ith frame, W 1 with μ 1 , Σ 1 and the remaining part, W 2 , with a second Gaussian μ 2 , Σ 2 .This representation using a Gaussian process is not totally exact when abrupt changes are close to each other especially when the events to be detected are too short and impulsive.To solve this problem, our proposed technique uses 1-SVMs and exponential family model to maximize the generalized likelihood ratio with any probability distribution of windows.

Exponential family
The exponential family covers a large number (and wellknown classes) of distributions such as Gaussian, multinomial, and poisson.A general representation of an exponential family is given by the following probability density function: where h(x) is called the base density which is always ≥ 0, η is the natural parameter, T(x) is the sufficient statistic vector, and A(η) is the cumulant generating function or the log normalizer.
The choice of T(x) and h(x) determines the member of the exponential family.Also we know that since this is a density function, then For a Gaussian distribution, . Thus, Gaussian distribution is included in the exponential family.
The density function of an exponential family can be written in the case of presence of a reproducing kernel Hilbert space H with a reproducing kernel k as (10) with

Applying 1-SVM to sound detection
Novelty change detection theory using SVM and exponential family was first proposed in [40,41].In this paper, this problem will be addressed with novel sophisticated approaches.Let X = {x 1 , x 2 , . . ., x N } and Y = {y 1 , y 2 , . . ., y N } be two adjacent windows of acoustic feature vectors extracted from the audio signal, where N is the number of data points in one window.Let Z denote the union of the contents of the two windows having 2N data points.The sequences of random variables X and Y are distributed according to Px and Py distribution, respectively.We want to test if there exists a sound change after the sample x N between the two windows.
The problem can be viewed as testing the hypothesis H 0 : P x = P y against the alternative H 1 : Px / = Py.H 0 is the null hypothesis and represents that the entire sequence is drawn from a single distribution, thus there exists only one sound.While H 1 represents the hypothesis that there is a segment boundary after sample X n , the likelihood ratio test of this hypotheses test is the following: Since both densities are unknown, the generalized likelihood ratio (GLR) has to be used: where P 0 and P 0 are the maximum likelihood estimates of the densities.
Assuming that both densities P x and P y are included in the generalized exponential family, thus there exists a reproducing kernel Hilbert space H embedded with the dot product •, • H with a reproducing kernel k such that in (10): Using 1-SVM and the exponential family, a robust approximation of the maximum likelihood estimates of the densities P x and P y can be written as where α (x) i is determined by solving the one 1-SVM problem on the first half of the data (z 1 to z N ), while α (y) i is given by solving the 1-SVM problem on the second half of the data 6 EURASIP Journal on Advances in Signal Processing (z N+1 to z 2N ).Using these three hypotheses, the generalized likelihood ratio test is approximated as follows: A sound change in the frame z n exists if where s x is a fixed threshold.Moreover, 2N i=N+1 α (y) i k(z j , z i ) is very small and can be neglected in comparison with N i=1 α (x)  i k(z j , z i ).Then a sound change is detected when

Sound detection criterion
Previously, we showed that a sound change exists if the condition defined by ( 18) is verified.This sound detection approach can be interpreted like this: to decide if a sound change exits between the two windows X and Y , we built an SVM using the data X as learning data, then Y data are used for testing if the two windows are homogenous or not.
On the other hand, since H 0 represents the hypothesis of P x = P y , the likelihood ratio test of the hypotheses test described previously can be written as Using the same gait, a sound change has occurred if Preliminary empirical tests show that in some cases it is more appropriate to apply two training rounds: after using X data for learning and Y data for testing, we can use Y data for learning and X data for testing.This procedure provides more detection accuracy.For that reason, it is more appropriate to use the criterion described as follow: where S = s x + s y .Equation ( 21) can be considered as a distance measure between two datasets.Obviously, higher values of this distance indicate that the two dataset distributions are not similar.

Our sound detection method
Our technique of sound detection is based on the computation of the distance detailed in (21) between a pair of adjacent windows of the same size shifted by a fixed step along the whole parameterized signal.This allows to obtain the curve of the variation of the distance in time.The analysis of this curve shows that a sound change point is characterized by the presence of a "significant" peak.A peak is regarded as "significant" when it presents a high value.So, break points can be detected easily by searching the local maxima of the distance curve that presents a value higher than a fixed threshold (Figure 3).

APPLICATION OF 1-SVMs TO SOUNDS CLASSIFICATION
In audio classification systems, the most popular approach is based on hidden Markov models (HMMs) with Gaussian mixture observation densities.These systems typically use a representational model based on maximum likelihood decoding and expectation maximization-based training.Though powerful, this paradigm is prone to overfitting and does not directly incorporate discriminative information.It is shown that HMM-based sound recognition systems perform very well on closed-loop tests but performance degrades significantly on open-loop tests.In [42], we showed that this is specially true for impulsive sound classification.As an attempt to overcome these drawbacks, artificial neural networks (ANNs) have been proposed as a replacement for the Gaussian emission probabilities under the belief that the ANN models provide better discrimination capabilities.However, the use of ANNs often results in overparameterized models which are also prone to overfitting.This can be attributed to the fact that most systems do not generalize well.We need systems with good generalization properties where the worst case performance on a given test set can be bounded as part of the training process without having to actually test the system.With many realworld applications where open-loop testing is required, the significance of generalization is further amplified.
The application addressed here concerns real-world sound classification.In real environment, there might be many sounds which do not belong to one of the predefined classes, thus it is necessary to define a rejection class, which may gather all sounds which do not belong to the training classes.An easy and elegant way to do so consists of estimating the regions of high probability of the known classes in the space of features, and considering the rest of the space as the rejection class.Training several 1-SVMs does this automatically.
In order to enhance the discrimination ability of the proposed classification method, the discrimination rule illustrated by (6) will be replaced by a sophisticated dissimilarity measure described in the subsection below.

A dissimilarity measure
The 1-SVM can be used to learn the MVS of a dataset of feature vectors which relate to sounds.In the following, we will define a dissimilarity measure by adapting the results of [13,15].Assume that N 1-SVMs have been learnt from the datasets {X 1 , . . ., X N }, and consider one of them, with associated set of coefficients denoted ({α j } j=1,...,m , ρ).In order to determine whether a new datum x is similar to the set X, we will define a dissimilarity measure, denoted by d(X, x), and deduced from the decision function f X (x) = m j=1 α j k(x j , x) − ρ, in which ρ is seen as a scaling parameter which balances the α j 's.Thanks to this normalization, the comparison of such dissimilarity measures d(X i , x) and d(X i , x) is possible.Indeed, because k(x, •) H = 1, where w(•)∠k(x, •) denotes the angle between w(•) and k(x, •).
By doing elementary geometry in feature space, we can show that ρ/ w(•) H = cos( θ) (Figure 2).This yields the following interpretation of d(X, x): Finally, the following relation shows that the normalization is sound, and makes d(X, x) a valid tool to examine the membership of x to a given class represented by a training set X.

Multiple sound classes in 1-SVM-based classification algorithm
The sound classification algorithm comprises three main steps.
Step one is that of training data preparation, and it includes the selection of a set of features which are computed for all the training data.The value of ν is selected in the reduced interval [0.05, 0.8] in order to avoid edge effects for small or large values of ν.We adopt the following notations.We assume that X = {x 1 , . . ., x m } is a dataset in R d .Here, each x j is the full feature vector of a signal, that is, each signal is represented by one vector x j in R d .Let X be the set of training sounds, shared in N c classes denoted by X 1 , . . ., X Nc .Each class contains m i sounds, i = 1, . . ., N c .

Algorithm 1 (Sound classification algorithm).
Step 1 (Data preparation).(i) Select a set of features.
(ii) Form the training sets X i = {x i,1 , ..., x i,mi }, i = 1, . . ., N c by computing these features and forming the feature vectors for all the training sounds selected.
(iii) Set the parameter σ of the Gaussian RBF kernel to some pre-determined value (e.g., set σ as half the average euclidean distance between any two points x i, j and x i , j [3]), and select ν ∈ [0.05, 0.8].
Step 3 (Testing step).(i) For each sound s to be classified into one of the N c classes, do (1) compute its feature vector, denoted x, (2) for i = 1, . . ., N c , compute d(X i , x) by using ( 24), (3) assign the sound s to the class i such that i = arg min i=1,...,Nc d(X i , x).

Experimental setup
The major part of the sound samples used in the sound recognition experiments is taken from different sound libraries available on the market [43,44].Considering several sound libraries is necessary for building a representative, large, and sufficiently diversified database.Some particular classes of sounds have been built or completed with handrecorded signals.All signals in the database have a 16-bit resolution and are sampled at 44100 Hz.During database construction, great care was devoted to the selection of the signals.When a rather general use of the sound recognition system is required, some kind of intraclass diversity in the signal properties should be integrated in the database.Even if it would be better for a given sound recognition system, to be designed for the specific type of encountered signals, it was decided in this study to incorporate sufficiently diverse signals in the same category.As a result, one class of signals can be composed by very different temporal or spectral characteristics, amplitude levels, and duration and time location.
The selected sounds are impulsive and they are typical of surveillance applications.The number and duration of considered samples for each sound category is indicated in Table 1.
Furthermore, other nonimpulsive classes of sounds (machines, children voices) are also integrated in the experimentation.We note that the number of items in each class is deliberately not equal, and sometimes very different.Moreover, explosion and gunshot sounds are very close to each other.Even for a person, it is sometimes not obvious to discriminate between them.They are intentionally differentiated to test ability of the system in separating very close classes of sounds.

Sound detection experiments
This section presents sound detection results with experiments conducted on an audio stream with length more than 30 minutes containing the sounds (events) described in Table 1.After extracting the feature vectors (using a frame with length 25 ms and 50% overlap), a sliding analysis window of a fixed length was used.This value is the result of a tradeoff between the number of frames inside the analysis windows required for significant statistical estimation and for the fact that this analysis window must not contain more than one sound change point.The sounds to be detected are short and impulsive, thus the window analysis length was fixed to 1.4 seconds.
A change sound detection system has two possible types of error.Type-I-errors occur if a true change is not spotted within a certain window (missed detection).Type-II-errors occur when a detected change does not correspond to a true change in the reference (false alarm).Figure 4 illustrates an example of the missed detection, false alarm and changepoint tolerance evaluation for the audio detection task.In the conducted experiments, we considered that a change point is detected using a certain tolerance settled to 0.4 second.
Type-I and -II errors are also referred to as precision (PRC) and recall (RCL), respectively, wich are defined as PRC = Number of correctly found changes Total number of changes found , RCL = Number of correctly found changes Total number of correct changes . ( In order to compare the performance of different systems, the F-measure is often used and is defined as The F-measure varies from 0 to 1, with a higher Fmeasure indicating better performance. The results using the proposed technique (1-SVM) and the other classical approaches (cross-correlation (CC), energy prediction (EP), wavelet filtering (WF), and BIC) are presented below.All the studied techniques use a threshold that must be fixed empirically and the experimental curves were obtained by varying this threshold.In theory, the BIC-based method did not use any threshold.However, in previous works [20], it has been shown that the ΔBIC uses a parameter λ that must be settled empirically and this parameter was considered as a hidden threshold.Figure 5 presents a recall (RCL) versus a precision (PRC) plot for the different studied methods.We can notice that the proposed 1-SVM-based sound detection method outperforms the others.Figures 6 and 7 illustrate the performance of the detection with different MFCC orders.This study experimented on three different MFCC orders: 13, 26, and 39.Generally, the 13 MFCCs include 12 MFCCs and onelog energy.The 26 MFCCs include the 13 MFCCs and their firsttime derivatives, and the 39 MFCCs include the 13 MFCCs and theirs first-and second-time derivatives.As presented in Figure 6, the features with higher dimensions give fewer errors in parameter estimation and better detection performance.This is due to the fact that 1-SVMs are not sensitive to the dimensionality of the feature vectors.However, using 26 MFCCs and 39 MFCCs with BIC gives low values of PRC and RCL compared to those obtained using 13 MFCCs.
The best results achieved using all the studied methods are illustrated in Table 2.The PRC and RCL values obtained with the sound detection method based on BIC are lower than the proposed method (PRC = 0.72, RCL = 0.73).This is due essentially to the presence of short sounds that can be close to each others.In this case, we do not have enough data for the good estimation of the BIC parameters.To avoid this deficiency, we used 1-SVMs with the exponential family.
Results obtained with cross-correlation, energy prediction, and wavelet filtering methods show that using only an energy-based criterion to detect events is not very appropriate when there are sounds that present similar characteristics and which are very close to each others.With wavelet filtering, a slightly better result was obtained because it leads to better characterize the acoustical properties of complex audio scenes.
Sound detection using the proposed method based on 1-SVMs presents better results than all the other techniques.In  fact, the obtained higher value of PRC (0.86) indicates that our technique avoids many false alarms.Moreover, by using this method, we can detect approximately the major break points that exist in the audio stream (higher RCL = 0.85).

Sound classification experiments
In this section, we will present classification results obtained by applying Algorithm 1. Features are computed from all the samples in each sound (segment).The analysis window is Hamming with length 25 milliseconds and 50% overlap.The selected feature vector contains 12 Mel-frequency cepstral coefficients (MFCCs), the energy, the Logenergy, the Spectral Centrod (SC), and the spectral rolloff point (SRF).More details about these features and theirs computations can be found in our previous work [24,45].The used database is illustrated in Table 1, 70% of the samples are used for the training set and 30% for the testing set.
Evaluations on the 1-SVM-based system using a Gaussian RBF kernel with individual features are compared to the results obtained by the M-SVM-based classifiers (multiclass) and by a baseline HMM-based classifier.
A multiclass pattern sound recognition system can be obtained from two-class SVMs.The basis theory of SVM for two-class classification in beyond the scope of this paper (see our previous works for more details [46]).There are generally two schemes for this purpose.One is the one-versus-all (1-vs-all) strategy to classify between each class and all the remaining; the other is the one-versus-one (1-vs-1) strategy to classify between each pair.However, the best method of extending the two-class classifier to multiclass problems is not clear.The 1-vs-all approach works by constructing for each class a classifier which separates that class from the remainder of the data.A given test example is then classified as belonging to the class whose boundary maximizes the margin.The 1-vs-1 approach simply constructs for each pair of classes a classifier which separates those classes.A test example is then classified by all of the classifiers, and is said to belong to the class with the largest number of positive outputs from these subclassifiers.
Moreover, for a complete comparison task between classifiers, we choose to train a statistical model for each audio class using multi-Gaussian hidden Markov models (HMMs).More details about HMMs can be found in our previous work [42], where we reported an advanced application of adapted HMMs for sounds classification.During training, by analyzing the feature vectors of the training set, the parameters for each state of an audio model are estimated using the well-known Baum-Welch algorithm [22].The procedure starts with random initial values for all of the parameters and optimizes the parameters by iterative reestimation.Each iteration runs through the entire set of training data in a process that is repeated until the model converges to satisfactory values [21,47].A specific HMM topology is used to describe how the states are connected.The temporal structures of audio sequences for an isolated sound recognition problem require the use of a simple left-right topology with five states in total.Three of these are emitting states and have output probability distributions associated with them.Our system uses continuous density models in which each observation probability distribution is represented by a mixture Gaussian density.The optimum number of mixture components N G in each state is reached by applying a mixture incrementing.
Tables 3-6 present some confusion matrices illustrating the best results for the different tested classifiers.The performance rate is computed as the percentage number of sounds correctly recognized and it is given by (H/N)×100%, where H is the number of correct sounds and N is the total number of sounds to be recognized.
In order to provide a comparison point, we conducted experiments using HMMs, M-SVM(1-vs-1), and M-SVM(1vs-all).By comparison with the other studied classifiers, the use of 1-SVMs is plainly justified by the results presented here, as it yields consistently lower-error rate and a highclassification accuracy.
Due to the need to estimate several classifiers, if we used 1-vs-1 or 1-vs-all approaches to solve an N-class classification problem in computationally restricted environments this can be a serious impediment.In conclusion, though SVMs are well-founded mathematically to achieve good generalization while maintaining a high-classification accuracy, we need to consider issues such as computation complexity and ease of implementation in order to choose the best classifier approach for a given application.
1-vs-1 classifiers learn to discriminate one class from another class and 1-vs-all classifiers learn to discriminate one class from all other classes.1-vs-1 classifiers are typically smaller and can be estimated using fewer resources than 1vs-all classifiers.When the number of classes is N we need to estimate N(N − 1)/2 1-vs-1 classifiers as compared to 1vs-all classifiers.On several standard classification tasks, it has been proven that 1-vs-1 classifiers are marginally more accurate than 1-vs-all classifiers.In most cases, the number of 1-vs-1 classifiers that need to be estimated is significantly greater that 1-vs-all classifiers and estimating these classifiers can be very time consuming.In fact, using 1-vs-1 classifiers makes each individual training problem smaller, and hence the memory CPU time required to train each classifier is greatly reduced, but the number of classifiers to be trained is high.While using a 1-vs-all approach requires many fewer classifiers to be trained, the memory requirements to train each classifier were found to be prohibitive.We used both 1vs-1 and 1-vs-all classifiers in our experiments reported here in order to apply a complete comparison with the proposed 1-SVM classifier.Overall, we found the 1-SVM methodology more easy to implement and tune and well adapted to large dimensional feature vectors, while having a reasonable training cost.
The SVM model has two parameters that have to be adjusted: ν and σ.We first addressed the problem of tuning the kernel parameter σ.There are several possible criterions for selecting σ such as minimizing the number of support vectors, maximizing the margin of separation from the origin, and minimizing the radius of the smallest sphere enclosing the data [48].Figure 8 shows a plot of the second criterion as a function of σ.As can be seen, using validation sets to do cross-validation is of course a good way to tune the kernel parameter, σ.From the dataset, we were able to make validation sets and use them to examine the classification accuracy of the classifier as a function of σ.For a sufficiently large training set, it is possible to select the optimal parameters by applying an original cross-validation procedure [49].σ must be tuned to control the amount of smoothing because the good performance of RBF kernels highly relies on the choice of this parameter.Figure 8 shows the performance of 1-SVMs using an RBF kernel versus σ.It is interesting to point out the behavior of a 1-SVM with an RBF kernel when σ becomes too small and when it becomes too large.When σ becomes too small, all the training examples are support vectors.This means that the 1-SVM learns by heart and then is unable to generalize.But, when σ becomes too large, the RBF kernel will be equivalent to the linear kernel and this leads to flat decision boundaries.
We conducted also some experiences in Table 7 to show the effect of the parameter ν.The 1-SVM algorithm performs well with the small values of ν.Since the smaller values of ν correspond to the smaller number of outliers, this leads to the larger region capturing most of the training points.It was decided (Table 7) to only allow 20% classification error on the training data, that is, ν = 0.2.
We can remark that splitting the multiclass problem into several two classes subproblems is an approach which is generally quite precise when the number of classes is small (typically up to 5), and when the number of training data is reasonable.Indeed, all the data of all classes are used to train the multiclass SVM, which scales typically from O(( Nc i=1 Nc i =1,...,N ) i / =i (m i + m i ) 3 ) to O(( Nc i=1 m i ) 3 ) (each class i contains m i sounds).However, the 1-SVM approach can be generalized to any number of classes, and the computational cost for training scales with O( Nc i=1 m 3 i ), which may be far quicker than any of the multiple class approaches.
In conclusion, due to the need to estimate several classifiers if using 1-vs-1 or 1-vs-all approaches to solve an N-class classification problem, in computationally restricted environments, this can be a serious impediment.Thus, though SVMs are well founded mathematically to achieve good generalization while maintaining a high-classification accuracy, we need to consider issues such as computation complexity and ease of implementation in order to choose the best classifier approach for a given application.Hence, in situations where accuracy and generalization are the only most important criterions for selection, we can confirm that both M-SVM strategies should be explored.In the literature, 1-vs-1 classifiers had been shown to perform better than 1-vs-all classifiers in many classification tasks.This conclusion is also confirmed in Table 7.There are, however, other practical issues for this choice, using 1-vs-1 classifiers makes the problem of each individual training smaller, and hence the memory CPU time required to train each classifier is greatly reduced.While using a 1-vs-all approach requires many fewer classifiers to be trained, the memory requirements to train each classifier were found to be prohibitive.

CONCLUSION
In this paper, we have proposed a new unsupervised sound detection algorithm based on 1-SVMs.This algorithm outperforms classical sound detection methods.Using the exponential family model, we obtain a good estimation of the generalized likelihood ratio applied on the known hypothesis test generally used in change-detection tasks.Experimental results present higher precision and recall values than those obtained with classical sound detection techniques.Moreover, we have developed a multiclass classification strategy by using 1-SVMs to solve a sound classification problem.The proposed system uses a discriminative method based on a sophisticated dissimilarity measure, in order to classify a set of sounds into predefined classes.
There is still room for improvement in the proposed approaches.In particular, our future research will be focused on addressing the following issues.First, in order to process in real time, the available data to train models either for sound detection or classification are always limited.Estimating an accurate model from limited training data is still a challenge.Also, in real-world conditions, the complexity of the application context affects negatively segmentation and classification results.

Figure 1 :Figure 2 :
Figure1: The event recognition process is composed into two main tasks: the sound detection task and the sound classification task.As illustrated in (a), an unsupervised algorithm based on 1-SVMs will be applied to address the event detection task.In (b), a supervised learning classification algorithm based on 1-SVMs will be proposed.

Figure 3 :
Figure 3: Block diagram of our sounds detection approach.The method is based on a new distance measure d between two adjacent analysis windows.This distance is the sum of d 1 in (18) and d 2 in (20).d 1 is obtained by using training dataset from the first window and testing dataset from the second one.d 2 is computed by inverting the datasets.

Figure 4 :
Figure 4: Example of a missed detection and a false alarm of a change point.

9 RCLFigure 5 :
Figure 5: RCL versus PRC curves of the proposed 1-SVMs-based sound detection methods against the other classical approaches.

Figure 8 :
Figure 8: Influence of the parameter σ in a Gaussian RBF kernel on the accuracy of the proposed 1-SVM-based classification task, when using validation sets and an iteration number P, as detailed in Algorithm 1.

Table 1 :
Classes of sounds and number of samples in the database used for performance evaluation.

Table 2 :
Sound detection results using various techniques.

Table 6 :
Confusion Matrix obtained with HMMs (N G = 3 and 5 iterations in the Baum-Welch algorithm are applied) using a feature vector containing 12 cepstral coefficients MFCC + Energy + Logenergy + SC + SRF.

Table 7 :
Sound recognition rates for various values of ν applied to 1-SVMs-and M-SVMs-based classifiers.