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

作者：Ingrassia Salvatore^*; Rocci Roberto

来源：Computational Statistics & Data Analysis, 2011, 55(4): 1715-1725.

DOI：10.1016/j.csda.2010.10.026

• Mixture models
• EM algorithm
• Degeneracy
• Dynamic constraints

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.

• 出版日期2011-4-1