EM algorithms for multivariate normal mixture decomposition have been recently proposed in order to maximize the likelihood function in a constrained parameter space having no singularities and a reduced number of spurious local maxima. However, such approaches require some a priori information about the eigenvalues of the covariance matrices. The behavior of the EM algorithm near a degenerated solution is investigated. The obtained theoretical results would suggest a new kind of constraint based on the dissimilarity between two consecutive updates of the eigenvalues of each covariance matrix. The performances of such a ‘‘dynamic’’ constraint are evaluated on the grounds of some numerical experiments.

Degeneracy of the EM algorithm for the MLE of multivariate Gaussian mixtures and dynamic constraints

INGRASSIA, Salvatore;
2011

Abstract

EM algorithms for multivariate normal mixture decomposition have been recently proposed in order to maximize the likelihood function in a constrained parameter space having no singularities and a reduced number of spurious local maxima. However, such approaches require some a priori information about the eigenvalues of the covariance matrices. The behavior of the EM algorithm near a degenerated solution is investigated. The obtained theoretical results would suggest a new kind of constraint based on the dissimilarity between two consecutive updates of the eigenvalues of each covariance matrix. The performances of such a ‘‘dynamic’’ constraint are evaluated on the grounds of some numerical experiments.
Mixture models; EM algorithm; Dynamic constraints
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/9666
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