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

Chamroukhi, Faïcel; Samé, Allou; Govaert, Gérard; Aknin, Patrice

doi:10.1016/j.neucom.2009.12.023

Cited by 46 publications

(66 citation statements)

References 25 publications

(43 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…through the well known Iteratively Reweighted Least Squares (IRLS) algorithm (Green 1984;Chamroukhi et al 2010). Let us recall that the IRLS algorithm, which is generally used to estimate the parameters of a logistic regression model, is equivalent to the following Newton Raphson algorithm (Green 1984;Chamroukhi et al 2010):…”

Section: M-step (Maximization)mentioning

confidence: 99%

“…Let us recall that the IRLS algorithm, which is generally used to estimate the parameters of a logistic regression model, is equivalent to the following Newton Raphson algorithm (Green 1984;Chamroukhi et al 2010):…”

Section: M-step (Maximization)mentioning

confidence: 99%

“…Within the particular context of time series with changes in regime, a specific regression model has been proposed in Chamroukhi et al (2010) to model time series with changes in regime. The model in question is a regression model in which the polynomial coefficients may vary according to a discrete hidden process, and which uses logistic functions to model the (smooth or abrupt) transitions between regimes.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Model-based clustering and segmentation of time series with changes in regime

Samé

Chamroukhi

Govaert

et al. 2011

Adv Data Anal Classif

Self Cite

View full text Add to dashboard Cite

Mixture model-based clustering, usually applied to multidimensional data, has become a popular approach in many data analysis problems, both for its good statistical properties and for the simplicity of implementation of the Expectation-Maximization (EM) algorithm. Within the context of a railway application, this paper introduces a novel mixture model for dealing with time series that are subject to changes in regime. The proposed approach, called ClustSeg, consists in modeling each cluster by a regression model in which the polynomial coefficients vary according to a discrete hidden process. In particular, this approach makes use of logistic functions to model the (smooth or abrupt) transitions between regimes. The model parameters are estimated by the maximum likelihood method solved by an Expectation-Maximization algorithm. This approach can also be regarded as a clustering approach which operates by finding groups of time series having common changes in regime. In addition to providing a time series partition, it therefore provides a time series segmentation. The problem of selecting the optimal numbers of clusters and segments is solved by means of the Bayesian Information Criterion (BIC). The ClustSeg approach is shown to be efficient using a variety of simulated time series and real-world time series of electrical power consumption from rail switching operations. Mixture model, Regression mixture, Hidden logistic proces

show abstract

Section: M-step (Maximization)mentioning

confidence: 99%

Section: M-step (Maximization)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Model-based clustering and segmentation of time series with changes in regime

Samé

Chamroukhi

Govaert

et al. 2011

Adv Data Anal Classif

Self Cite

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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 ...

show abstract

Distance‐weighted discrimination for functional data

Sang

2023

Stat

View full text Add to dashboard Cite

The main contribution of the paper is the development of a new margin‐based classifier called distance‐weighted discrimination (DWD) for functional data classification. The proposed classifier employs functional principal component analysis (FPCA) to reduce the dimensionality of the functional data and is free of the restrictive assumptions imposed by Bayes classifiers in terms of mean and covariance functions. Theoretical results show that the proposed classifier is Bayes risk consistent under mild assumptions. Simulation studies and real data examples demonstrate that the DWD classifier outperforms several conventional classifiers in terms of prediction accuracy. Overall, the paper provides a new approach for functional data classification with good empirical performance.

show abstract

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

Cited by 46 publications

References 25 publications

Model-based clustering and segmentation of time series with changes in regime

Model-based clustering and segmentation of time series with changes in regime

Finite mixture models for regression problems

Distance‐weighted discrimination for functional data

Contact Info

Product

Resources

About