Allou Samé

A hidden process regression model for functional data description. Application to curve discrimination

A new approach for functional data description is proposed in this paper. It consists of a regression model with a discrete hidden logistic process which is adapted for modeling curves with abrupt or smooth regime changes. The model parameters are estimated in a maximum likelihood framework through a dedicated expectation maximization (EM) algorithm. From the proposed generative model, a curve discrimination rule is derived using the maximum a posteriori rule. The proposed model is evaluated using simulated curves and real world curves acquired during railway switch operations, by performing comparisons with the piecewise regression approach in terms of curve modeling and classification.

2009 Special Issue: Time series modeling by a regression approach based on a latent process

Time series are used in many domains including finance, engineering, economics and bioinformatics generally to represent the change of a measurement over time. Modeling techniques may then be used to give a synthetic representation of such data. A new approach for time series modeling is proposed in this paper. It consists of a regression model incorporating a discrete hidden logistic process allowing for activating smoothly or abruptly different polynomial regression models. The model parameters are estimated by the maximum likelihood method performed by a dedicated Expectation Maximization (EM) algorithm. The M step of the EM algorithm uses a multi-class Iterative Reweighted Least-Squares (IRLS) algorithm to estimate the hidden process parameters. To evaluate the proposed approach, an experimental study on simulated data and real world data was performed using two alternative approaches: a heteroskedastic piecewise regression model using a global optimization algorithm based on dynamic programming, and a Hidden Markov Regression Model whose parameters are estimated by the Baum-Welch algorithm. Finally, in the context of the remote monitoring of components of the French railway infrastructure, and more particularly the switch mechanism, the proposed approach has been applied to modeling and classifying time series representing the condition measurements acquired during switch operations.

An online classification EM algorithm based on the mixture model

Abstract Mixture model-based clustering is widely used in many applications. In certain real-time applications the rapid increase of data size with time makes classical clustering algorithms too slow. An online clustering algorithm based on mixture models is presented in the context of a real-time flaw-diagnosis application for pressurized containers which uses data from acoustic emission signals. The proposed algorithm is a stochastic gradient algorithm derived from the classification version of the EM algorithm (CEM). It provides a model-based generalization of the well-known online k-means algorithm, able to handle non-spherical clusters. Using synthetic and real data sets, the proposed algorithm is compared with the batch CEM algorithm and the online EM algorithm. The three approaches generate comparable solutions in terms of the resulting partition when clusters are relatively well separated, but online algorithms become faster as the size of the available observations increases.

A classification EM algorithm for binned data

A real-time flaw diagnosis application for pressurized containers using acoustic emissions is described. The pressurized containers used are cylindrical tanks containing fluids under pressure. The surface of the pressurized containers is divided into bins, and the number of acoustic signals emanating from each bin is counted. Spatial clustering of high density bins using mixture models is used to detect flaws. A dedicated EM algorithm can be derived to select the mixture parameters, but this is a greedy algorithm since it requires the numerical computation of integrals and may converge only slowly. To deal with this problem, a classification version of the EM (CEM) algorithm is defined, and using synthetic and real data sets, the proposed algorithm is compared to the CEM algorithm applied to classical data. The two approaches generate comparable solutions in terms of the resulting partition if the histogram is sufficiently accurate, but the algorithm designed for binned data becomes faster when the number of available observations is large enough.

Recognition of gait cycle phases using wearable sensors

The analysis and monitoring of the human daily living activities plays an important role for rehabilitation goals, fall prevention rehabilitation and general health-care treatments. Among these activities, walking is the most important daily motion. Studying the evolution of the gait cycle through the analysis of the human center of force is beneficial to predict any abnormal walking pattern. The analysis is based on the use of pressure-based mapping system that collects pressure and force measurement during the gait cycle. This paper deals mainly with the detection of the main characteristics of the gait phases. To this end, a segmentation of the center of force of the human body measure through the in-shoe pressure mapping system is performed to identify the gait phases. The proposed segmentation approach consists in modeling each segment by a regression model and using logistic functions to model the transitions between segments. This flexible modeling through the logistic functions has the advantage of detecting abrupt and smooth transitions between segments. This paper deals with the detection of the main characteristics of the gait phases.A segmentation of the human body COF is done using the in-shoe pressure mapping system.Identification of the gait phases is done using a regression model.The proposed method has the advantage of detecting abrupt and smooth transitions.The proposed method is implemented and verified by experiment tests.

Model-based functional mixture discriminant analysis with hidden process regression for curve classification

In this paper, we study the modeling and the classification of functional data presenting regime changes over time. We propose a new model-based functional mixture discriminant analysis approach based on a specific hidden process regression model that governs the regime changes over time. Our approach is particularly adapted to handle the problem of complex-shaped classes of curves, where each class is potentially composed of several sub-classes, and to deal with the regime changes within each homogeneous sub-class. The proposed model explicitly integrates the heterogeneity of each class of curves via a mixture model formulation, and the regime changes within each sub-class through a hidden logistic process. Each class of complex-shaped curves is modeled by a finite number of homogeneous clusters, each of them being decomposed into several regimes. The model parameters of each class are learned by maximizing the observed-data log-likelihood by using a dedicated expectation-maximization (EM) algorithm. Comparisons are performed with alternative curve classification approaches, including functional linear discriminant analysis and functional mixture discriminant analysis with polynomial regression mixtures and spline regression mixtures. Results obtained on simulated data and real data show that the proposed approach outperforms the alternative approaches in terms of discrimination, and significantly improves the curves approximation.

A regression model with a hidden logistic process for feature extraction from time series

A new approach for feature extraction from time series is proposed in this paper. This approach consists of a specific regression model incorporating a discrete hidden logistic process. The model parameters are estimated by the maximum likelihood method performed by a dedicated Expectation Maximization (EM) algorithm. The parameters of the hidden logistic process, in the inner loop of the EM algorithm, are estimated using a multi-class Iterative Reweighted Least-Squares (IRLS) algorithm. A piecewise regression algorithm and its iterative variant have also been considered for comparisons. An experimental study using simulated and real data reveals good performances of the proposed approach.

Model-based clustering with Hidden Markov Model regression for time series with regime changes

This paper introduces a novel model-based clustering approach for clustering time series which present changes in regime. It consists of a mixture of polynomial regressions governed by hidden Markov chains. The underlying hidden process for each cluster activates successively several polynomial regimes during time. The parameter estimation is performed by the maximum likelihood method through a dedicated Expectation-Maximization (EM) algorithm. The proposed approach is evaluated using simulated time series and real-world time series issued from a railway diagnosis application. Comparisons with existing approaches for time series clustering, including the stand EM for Gaussian mixtures, K-means clustering, the standard mixture of regression models and mixture of Hidden Markov Models, demonstrate the effectiveness of the proposed approach.

Mixture-model-based signal denoising

This paper proposes a new signal denoising methodology for dealing with asymmetrical noises. The adopted strategy is based on a regression model where the noise is supposed to be additive and distributed following a mixture of Gaussian densities. The parameters estimation is performed using a Generalized EM (GEM) algorithm. Experimental studies on simulated and real signals in the context of a diagnosis application in the railway domain reveal that the proposed approach performs better than the least-squares and wavelets methods.

A mixture model-based on-line CEM algorithm

An original on-line mixture model-based clustering algorithm is presented in this paper. The proposed algorithm is a stochastic gradient ascent derived from the Classification EM (CEM) algorithm. It generalizes the on-line k-means algorithm. Using synthetic data sets, the proposed algorithm is compared to CEM and another on-line clustering algorithm. The results show that the proposed method provides a fast and accurate estimation when mixture components are relatively well separated.