An Expectation–Maximization algorithm for the Wishart mixture model: Application to movement clustering

This article presents an Expectation–Maximization algorithm for the Wishart mixture model in which realizations are matrices. Given a set of matrices, an iterative algorithm for estimating the parameters of such a mixture model is proposed. The obtained estimates can be interpreted in terms of mean...

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Veröffentlicht in:Pattern recognition letters Jg. 31; H. 14; S. 2318 - 2324
Hauptverfasser: Hidot, Sullivan, Saint-Jean, Christophe
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 15.10.2010
Elsevier
Schlagworte:
Applied sciences
Clustering
Computer Science
Detection, estimation, filtering, equalization, prediction
EM algorithm
Engineering Sciences
Exact sciences and technology
Information, signal and communications theory
Movement recognition
Second-order cross moments
Signal and communications theory
Signal and Image Processing
Signal representation. Spectral analysis
Signal, noise
Telecommunications and information theory
Wishart mixture model
Second-order cross moments
Wishart mixture model
Movement recognition
Clustering
EM algorithm
Second order
Automatic classification
Parameter estimation
Mixture theory
Iterative method
Scale factor
Signal classification
A posteriori estimation
Geometrical method
ISSN:0167-8655, 1872-7344
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Beschreibung
Zusammenfassung:This article presents an Expectation–Maximization algorithm for the Wishart mixture model in which realizations are matrices. Given a set of matrices, an iterative algorithm for estimating the parameters of such a mixture model is proposed. The obtained estimates can be interpreted in terms of mean matrices and scale factors. By applying the maximum a posteriori rule, we get an algorithm for the clustering of a set of matrices. This mixture model is then modified in order to deal with a set of samples. Unfortunately, the samples may be of different sizes. We propose to tackle this problem by considering the cross-product matrix as a signature for each sample. This set of cross-product matrices may be fitted with the proposed Wishart pseudo-mixture model in which the scale parameters of the distribution are not estimated but fixed. Again, we easily get a clustering algorithm from final parameter estimates. The different estimators are studied empirically through an analysis of their bias and variance and are validated onto an artificial dataset. Finally, we apply the Wishart pseudo-mixture model for analyzing motion-captured movements. Given the successive 3D positions of markers over the time, a cross-product matrix is constructed for each movement and put into the proposed classifier. We observe that the recognition rates are higher with our proposed approach than those with other geometric methods. Limits and constraints of the provided models are finally discussed.
ISSN:0167-8655
1872-7344
DOI:10.1016/j.patrec.2010.07.002