AMOUD , Hassan

The autoregressive (AR) model is a well-known technique to analyze time series. The Yule-Walker equations provide a straightforward connection between the AR model parameters and the covariance function of the process. In this paper, we propose a nonlinear extension of the AR model using kernel machines. To this end, we explore the Yule-Walker...

Moreover, in order to have a physical interpretation, some constraints should be incorporated in the signal or image processing technique, such as the non-negativity of the solution. This paper deals with the non-negative pre-image problem in kernel machines, for nonlinear pattern recognition. While kernel machines operate in a feature space,...

One may monitor the heart normal activity by analyzing the electrocardiogram. We propose in this paper to combine the principle of kernel machines, that maps data into a high dimensional feature space, with the autoregressive (AR) technique defined using the Yule-Walker equations, which predicts future samples using a combination of some...

Autoregressive (AR) modeling is a very popular method for time series analysis. Being linear by nature, it obviously fails to adequately describe nonlinear systems. In this paper, we propose a kernel-based AR modeling, by combining two main concepts in kernel machines. One the one hand, we map samples to some nonlinear feature space, where an...

L'analyse et la prédiction de séries temporelles par un modèle autorégressif ont été largement étudiées pour des systèmes linéaires. Toutefois, ce principe s'avère généralement inadapté pour l'analyse des systèmes non-linéaires. L'objectif de cette communication est de proposer un modèle autorégressif non-linéaire dans un espace de Hilbert à...

The inherent physical characteristics of many real-life phenomena, including biological and physiological aspects, require adapted nonlinear tools. Moreover, the additive nature in some situations involve solutions expressed as positive combinations of data. In this paper, we propose a nonlinear feature extraction method, with a non-negativity...

Rules of physics in many real-life problems force some constraints to be satisfied. This paper deals with nonlinear pattern recognition under non-negativity constraints. While kernel principal component analysis can be applied for feature extraction or data denoising, in a feature space associated to the considered kernel function, a pre-image...

Testing stationarity is an important issue in signal analysis and classification. Recently, time-frequency analysis has been investigated to detect the nonstationarity of a given signal, by constructiing from it a set of surrogate, stationarized signals. Time-frequency features are extracted to test the stationarity. Our paper is a further...

An operational framework is developed for testing stationarity relatively to an observation scale. The proposed method makes use of a family of stationary surrogates for defining the null hypothesis of stationarity. As a further contribution to the field, we demonstrate the strict-sense stationarity of surrogate signals and we exploit this...

The paper is concerned with the approach developed within the ANR Project StaRAC, and it gives an overview of its main results. The objective was to reconsider the concept of stationarity so as to make it operational, allowing for both an interpretation relatively to an observation scale and the possibility of its testing thanks to the use of...