Régis Lengellé

Joint recursive implementation of time-frequency representations and their modified version by the reassignment method

Abstract Cohens class time—frequency distributions (CTFDs) have significant potential for the analysis of non-stationary signals, even if the poor readability of their representations makes visual interpretations difficult. To concentrate signal components, Auger and Flandrin recently generalized the reassignment method (first applied to the spectrogram in the 1970s) to any bilinear representations. Unfortunately, this process is computationally expensive. In order to reduce computation time and to improve representations readability, we first introduce a new fast algorithm which allows the recursive evaluation of classical spectrograms and spectrograms modified by the reassignment method. In a second step, we show that rectangular, half-sine, Hamming, Hanning and Blackman functions can be used as running ‘short-time’ windows. Then the previous algorithm is extended to CTFDs. We show that the windows mentioned above can also be used to compute recursively reassigned smoothed pseudo-Wigner—Ville distributions. Finally, we show that the constraints on candidate windows are not very restrictive: any function (assumed periodic) can be used in practice as long as it admits a ‘short enough’ Fourier series decomposition.

Abnormal events detection using unsupervised One-Class SVM - Application to audio surveillance and evaluation -

This paper proposes an unsupervised method for real time detection of abnormal events in the context of audio surveillance. Based on training a One-Class Support Vector Machine (OC-SVM) to model the distribution of the normality (ambience), we propose to construct sets of decision functions. This modification allows controlling the trade-off between false-alarm and miss probabilities without modifying the trained OC-SVM that best capture the ambience boundaries, or its hyperparameters. Then we present an adaptive online scheme of temporal integration of the decision function output in order to increase performance and robustness. We also introduce a framework to generate databases based on real signals for the evaluation of audio surveillance systems. Finally, we present the performances obtained on the generated database.

Data-driven design and complexity control of time-frequency detectors

Abstract In this paper, we introduce a method of designing optimal time–frequency detectors from training samples, which is potentially of great benefit when few a priori information on the nonstationary signal to be detected is available. However, achieving good performance with data-driven detectors requires matching their complexity to the available amount of training samples: receivers with a too large number of adjustable parameters often exhibit a poor generalization performance whereas those with an insufficient complexity cannot learn all the information available in the design set. Then, using the principle of structural risk minimization proposed by Vapnik, we introduce procedures which provide powerful tools for tuning the complexity of generalized linear detectors and improving their performance. Next, these methods are successfully experimented on simulated and real data, with linear detectors operating in the time–frequency domain: it is in such high-dimensional feature spaces that procedures of deriving reduced-bias receivers from training samples are of prime necessity. Finally, we show that our methodology may offer a helpful support for designing detectors in many applications of current interest, such as biomedical engineering and complex systems monitoring.

An improved training algorithm for nonlinear kernel discriminants

A simple method to derive nonlinear discriminants is to map the samples into a high-dimensional feature space F using a nonlinear function and then to perform a linear discriminant analysis in F. Clearly, if F is a very high, or even infinitely, dimensional space, designing such a receiver may be a computationally intractable problem. However, using Mercer kernels, this problem can be solved without explicitly mapping the data to F. Recently, a powerful method of obtaining nonlinear kernel Fisher discriminants (KFDs) has been proposed, and very promising results were reported when compared with the other state-of-the-art classification techniques. In this paper, we present an extension of the KFD method that is also based on Mercer kernels. Our approach, which is called the nonlinear kernel second-order discriminant (KSOD), consists of determining a nonlinear receiver via optimization of a general form of second-order measures of performance. We also propose a complexity control procedure in order to improve the performance of these classifiers when few training data are available. Finally, simulations compare our approach with the KFD method.

Online Kernel Adaptive Algorithms With Dictionary Adaptation for MIMO Models

Nonlinear system identification has always been a challenging problem. The use of kernel methods to solve such problems becomes more prevalent. However, the complexity of these methods increases with time which makes them unsuitable for online identification. This drawback can be solved with the introduction of the coherence criterion. Furthermore, dictionary adaptation using a stochastic gradient method proved its efficiency. Mostly, all approaches are used to identify Single Output models which form a particular case of real problems. In this letter we investigate online kernel adaptive algorithms to identify Multiple Inputs Multiple Outputs model as well as the possibility of dictionary adaptation for such models.

Dictionary adaptation for online prediction of time series data with kernels

Kernel-based algorithms have been a topic of considerable interest in the machine learning community over the last ten years. Their attractiveness resides in their elegant treatment of nonlinear problems. They have been successfully applied to pattern recognition, regression and density estimation. A common characteristic of kernel-based methods is that they deal with kernel expansions whose number of terms equals the number of input data, making them unsuitable for online applications. Recently, several solutions have been proposed to circumvent this computational burden in time series prediction problems. Nevertheless, most of them require excessively elaborate and costly operations. In this paper, we investigate a new model reduction criterion that makes computationally demanding sparsification procedures unnecessary. The increase in the number of variables is controlled by the coherence parameter, a fundamental quantity that characterizes the behavior of dictionaries in sparse approximation problems. We incorporate the coherence criterion into a new kernel-based affine projection algorithm for time series prediction. We also derive the kernel-based normalized LMS algorithm as a particular case. Finally, experiments are conducted to compare our approach to existing methods.

On the linear relations connecting the components of the discrete Wigner distribution in the case of real-valued signals

It was shown that information conveyed by the discrete Wigner distribution is highly redundant, linear relations connecting its time-frequency components. This means that every component of the discrete Wigner distribution can be expressed as a linear combination of the elements of a basis. This set of generators consists of particular time-frequency components of the distribution. However, up to now, this basis and the associated linear map that allows to entirely generate the representation have still not been characterized. This problem is addressed in the case of real-valued signals. Results are illustrated by means of computer simulations. Finally, some extensions are pointed out.

F-SVR: A new learning algorithm for support vector regression

In this paper, we present a new method for optimizing support vector machines for regression problems. This algorithm searches for efficient feasible directions. Within these selected directions, we choose the best one, i.e. the one, coupled with an optimal step analytical evaluation, that ensures a maximum increase of the objective function. The resulting solution, the gradient and the objective function are recursively determined and the Gram matrix has not to be stored. Our algorithm is based on SVM-Torch proposed by Collobert for regression, which is similar to SVM-Light suggested by Joachims for classifications problems, but adapted to regression problems. We are also inspired by LASVM proposed by Bordes for classification problems. F-SVR algorithm uses a new efficient working set selection heuristic, ingeniously exploits quadratic function properties, so it is fast as well as easy to implement and is able to perform on large data sets.

Nonlinear Regularized Wiener Filtering With Kernels: Application in Denoising MEG Data Corrupted by ECG

Magnetoencephalographic and electroencephalographic recordings are often contaminated by artifacts such as eye movements, blinks, and cardiac or muscle activity. These artifacts, whose amplitude may exceed that of brain signals, may severely interfere with the detection and analysis of events of interest. In this paper, we consider a nonlinear approach for cardiac artifacts removal from magnetoencephalographic data, based on Wiener filtering. In recent works, nonlinear Wiener filtering based on reproducing kernel Hilbert spaces and the kernel trick has been proposed. However, the filter parameters are determined by the resolution of a linear system which may be ill conditioned. To deal with this problem, we introduce three kernel methods that provide powerful tools for solving ill-conditioned problems, namely, kernel principal component analysis, kernel partial least squares, and kernel ridge regression. A common feature of these methods is that they regularize the solution by assuming an appropriate prior on the class of possible solutions. We avoid the use of QRS-synchronous averaging techniques, which may induce distortions in brain signals if artifacts are not well detected. Moreover, our approach shows the nonlinear relation between magnetoencephalographic and electrocardiographic signals

Bayes-optimal detectors design using relevant second-order criteria

Statistical detection theories lead to the fundamental result that the optimum test consists in comparing any strictly monotone function of the likelihood ratio with a threshold value. In many applications, implementing such a test may be impossible. Therefore, we are often led to consider a simpler procedure for designing detectors. In particular, we can use alternative design criteria such as second-order measures of quality. A necessary and sufficient condition is given for such criteria to guarantee the best solution in the sense of classical detection theories. This result is illustrated by discussing the relevance of well-known criteria.