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

Chamroukhi, Faïcel; Glotin, H.; Samé, Allou

doi:10.1016/j.neucom.2012.10.030

Cited by 18 publications

(37 citation statements)

References 23 publications

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“…Methods of functional data analysis are becoming increasingly popular, e.g. in the cluster analysis (Jacques and Preda 2013;James and Sugar 2003;Peng and Müller 2008), classification (Chamroukhi et al 2013;Delaigle and Hall 2012;Mosler and Mozharovskyi 2015;Rossi and Villa 2006) and regression (Ferraty et al 2012;Goia and Vieu 2014;Kudraszow and Vieu 2013;Peng et al 2015;Rachdi and Vieu 2006;Wang et al 2015). Unfortunately, multivariate data methods cannot be directly used for functional data, because of the problem of dimensionality and difficulty in putting functional data into order.…”

Section: Introductionmentioning

confidence: 99%

Selected statistical methods of data analysis for multivariate functional data

et al. 2016

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Data in the form of a continuous vector function on a given interval are referred to as multivariate functional data. These data are treated as realizations of multivariate random processes. The paper is devoted to three statistical dimension reduction techniques for multivariate data. For the first one, principal components analysis, the authors present a review of a recent paper (Jacques and Preda in, Comput Stat Data Anal, 71:92-106, 2014). For two others one, canonical variables and discriminant coordinates, the authors extend existing works for univariate functional data to multivariate. These methods for multivariate functional data are presented, illustrated and discussed in the context of analyzing real data sets. Each of these techniques is applied on real data set.

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Section: Introductionmentioning

confidence: 99%

Selected statistical methods of data analysis for multivariate functional data

et al. 2016

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“…Here, we present a model that uses a logistic process rather than a Markov process. The resulting model is a MixRHLP (Chamroukhi, ; Chamroukhi et al, ; Samé et al, ).…”

Section: Latent Process Regression Mixtures For Functional Data Clustmentioning

confidence: 99%

“…Each curve represents the consumed power by the switch motor during each switch operation and the aim is to predict the state of the switch given a new operation data, or to cluster the times series to discover possible defaults. These data were studied in Chamroukhi (), Chamroukhi, Samé, Govaert, and Aknin (), Chamroukhi et al (, ), and Samé, Chamroukhi, Govaert, and Aknin (). Figure e shows n = 120 curves where each curve consists of m = 564 observations and Figure f shows n = 146 curves where each curve consists of m = 511 observations.…”

Section: Introductionmentioning

confidence: 99%

Model‐based clustering and classification of functional data

Chamroukhi

Nguyen

2019

WIREs Data Min & Knowl

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Complex data analysis is a central topic of modern statistics and learning systems which is becoming of broader interest with the increasing prevalence of high‐dimensional data. The challenge is to develop statistical models and autonomous algorithms that are able to discern knowledge from raw data, which can be achieved through clustering techniques, or to make predictions of future data via classification techniques. Latent data models, including mixture model‐based approaches, are among the most popular and successful approaches in both supervised and unsupervised learning. Although being traditional tools in multivariate analysis, they are growing in popularity when considered in the framework of functional data analysis (FDA). FDA is the data analysis paradigm in which each datum is a function, rather than a real vector. In many areas of application, including signal and image processing, functional imaging, bioinformatics, etc., the analyzed data are indeed often available in the form of discretized values of functions, curves, or surfaces. This functional aspect of the data adds additional difficulties when compared to classical multivariate data analysis. We review and present approaches for model‐based clustering and classification of functional data. We present well‐grounded statistical models along with efficient algorithmic tools to address problems regarding the clustering and the classification of these functional data, including their heterogeneity, missing information, and dynamical hidden structures. The presented models and algorithms are illustrated via real‐world functional data analysis problems from several areas of application. This article is categorized under: Fundamental Concepts of Data and Knowledge > Data Concepts Algorithmic Development > Statistics Technologies > Structure Discovery and Clustering

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“…For instance, it is possible to use the LMoLE to conduct clustering and discrimination of curves in the same manner as in Chamroukhi et al (2010) and Chamroukhi et al (2013), respectively. However, unlike the model of Chamroukhi et al (2013), we cannot trivially extend our methodology to handle the modeling of multiple correlated series simultaneously, although it may be possible to construct such a model using the multivariate generalization of Eltoft et al (2006) (see also Fang et al (1990, Section 3.5)); these functions are generally difficult to work with due to the modified Bessel function in their definitions.…”

Section: Chaptermentioning

confidence: 99%

“…Fourier basis regression for clustering by MLMMs (Ng et al, 2006), piecewise polynomial regression for clustering (Chamroukhi et al, 2010) and for classification Chamroukhi et al (2013), Gaussian process regression for classification by principal component analysis (Hall et al, 2001) and by centroid-based methods (Delaigle and Hall, 2012), support vector machines (SVMs) for classification (Rossi and Villa, 2006), and nonparametric density estimation for clustering (Boulle, 2012).…”

Section: Introductionmentioning

confidence: 99%

Finite mixture models for regression problems

Nguyen¹

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Finite mixture models (FMMs) are a ubiquitous tool for the analysis of heterogeneous data across a broad number of fields including agriculture, bioinformatics, botany, cell biology, economics, fisheries research, genetics, genomics, geology, machine learning, medicine, palaeontology, psychology, and zoology, among many others. Due to their flexibility, FMMs can be used to cluster data, classify data, estimate densities, and increasingly, they are also being used to conduct regression analysis and to analyze regression outcomes. There is now an expansive literature on the usage of FMMs for regression, as well as a broad demand for the development of such methods for the analysis of new and complex data.This thesis begins with a summary of the current literature on FMMs and their applications to regression problems. Here, the mixture of regression models (MRMs), cluster-weight models (CWMs), mixtures of experts (MoEs), and mixtures of linear of mixed effects models (MLMMs), as well as other variants of FMMs for regression analysis are introduced. Various properties such as denseness and identifiability, as well as maximum likelihood (ML) estimation techniques such as the expectation-maximization (EM) and minorization-maximization (MM) algorithms are discussed, and a review is presented regarding asymptotic inference and model selection in FMMs. A new result on the characterization of a t linear CWM (LCWM) is also presented. Some new applications of FMMs to regression problems are then discussed.Firstly, a series of models based on FMMs are presented for the clustering and classification of sparsely sampled bivariate functional data. These methods are named mixture of spatial spline regression (MSSR) and MSSR discriminant analysis (MSSRDA). MSSR is constructed using the theory of MLMMs and spatial splines, and an EM algorithm for the ML estimation of the model is presented. MSSRDA is then constructed by combining MSSR with the mixture discriminant analysis framework for classification. The methods are tested on their ability to cluster and classify simulated data. An example application to handwritten digits recognition is then presented. Here, it is shown that MSSR and MSSRDA perform comparably to currently available methods, and outperform said methods in missing data scenarios.Secondly, an FMM is used to produce a false discovery rate (FDR) control procedure for magnetic resonance imaging (MRI) data. In MRI data analysis, millions of hypotheses are often tested simultaneously, resulting in inflated numbers of false positive results. Many of the available FDR techniques for MRI data either do not take into account the spatial structure or rely on difficult to verify assumptions and user-specified parameters. To address these shortcomings, the Markov random field (MRF) FDR (MRF-FDR) technique is presented. MRF-FDR uses a Gaussian mixture model (GMM) to perform FDR control based on empirical-Bayesian principles. An MRF is then used to make the outcome of the GMM spatially coherent. The MRF is fitted using ...

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

Cited by 18 publications

References 23 publications

Selected statistical methods of data analysis for multivariate functional data

Selected statistical methods of data analysis for multivariate functional data

Model‐based clustering and classification of functional data

Finite mixture models for regression problems

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