A variational Expectation–Maximization algorithm for temporal data clustering

The problem of temporal data clustering is addressed using a dynamic Gaussian mixture model. In addition to the missing clusters used in the classical Gaussian mixture model, the proposed approach assumes that the means of the Gaussian densities are latent variables distributed according to random w...

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Bibliographic Details
Published inComputational statistics & data analysis Vol. 103; pp. 206 - 228
Main Authors El Assaad, Hani, Samé, Allou, Govaert, Gérard, Aknin, Patrice
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.2016
Elsevier
Subjects
Algorithms
Approximation
Clustering
Data Analysis, Statistics and Probability
Dynamic latent variable model
EM algorithm
Estimates
Gaussian
Kalman filter
Mathematical models
Maximum likelihood
Mixture model
Parameter estimation
Parameters
Physics
Temporal data clustering
Variational approximation
Kalman filter
Dynamic latent variable model
Mixture model
Variational approximation
Maximum likelihood
Clustering
EM algorithm
Temporal data clustering
DYNAMIC LATENT VARIABLE MODEL
TEMPORAL DATA CLUSTERING
CLUSTERING
MODELE DE MELANGE
ALGORITHME ESPERANCE-MAXIMISATION
FILTRE DE KALMAN
VARIATIONAL APPROXIMATION
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Summary:The problem of temporal data clustering is addressed using a dynamic Gaussian mixture model. In addition to the missing clusters used in the classical Gaussian mixture model, the proposed approach assumes that the means of the Gaussian densities are latent variables distributed according to random walks. The parameters of the proposed algorithm are estimated by the maximum likelihood approach. However, the EM algorithm cannot be applied directly due to the complex structure of the model, and some approximations are required. Using a variational approximation, an algorithm called VEM-DyMix is proposed to estimate the parameters of the proposed model. Using simulated data, the ability of the proposed approach to accurately estimate the parameters is demonstrated. VEM-DyMix outperforms, in terms of clustering and estimation accuracy, other state-of-the-art algorithms. The experiments performed on real world data from two fields of application (railway condition monitoring and object tracking from videos) show the strong potential of the proposed algorithms.
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ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2016.05.007