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The expectation-maximization (EM) algorithm is an iterative method forfinding maximum likelihood estimates when data are incomplete or are treated asbeing incomplete. The EM algorithm and its variants are commonly used forparameter estimation in applications of mixture models for clustering andclassification. This despite the fact that even the Gaussian mixture modellikelihood surface contains many local maxima and is singularity riddled.Previous work has focused on circumventing this problem by constraining thesmallest eigenvalue of the component covariance matrices. In this paper, weconsider constraining the smallest eigenvalue, the largest eigenvalue, and boththe smallest and largest within the family setting. Specifically, a subset ofthe GPCM family is considered for model-based clustering, where we use are-parameterized version of the famous eigenvalue decomposition of thecomponent covariance matrices. Our approach is illustrated using variousexperiments with simulated and real data.

Constrained Optimization for a Subset of the Gaussian Parsimonious Clustering Models