Model-based classification via mixtures of multivariate t-distributions

Authors:
Jeffrey L. Andrews;Paul D. McNicholas;Sanjeena Subedi
Affiliations:
Department of Mathematics and Statistics, University of Guelph, Ontario, Canada, N1G 2W1;Department of Mathematics and Statistics, University of Guelph, Ontario, Canada, N1G 2W1;Department of Mathematics and Statistics, University of Guelph, Ontario, Canada, N1G 2W1
Venue:
Computational Statistics & Data Analysis
Year:
2011

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Abstract

A novel model-based classification technique is introduced based on mixtures of multivariate t-distributions. A family of four mixture models is defined by constraining, or not, the covariance matrices and the degrees of freedom to be equal across mixture components. Parameters for each of the resulting four models are estimated using a multicycle expectation-conditional maximization algorithm, where convergence is determined using a criterion based on the Aitken acceleration. A straightforward, but very effective, technique for the initialization of the unknown component memberships is introduced and compared with a popular, more sophisticated, initialization procedure. This novel four-member family is applied to real and simulated data, where it gives good classification performance, even when compared with more established techniques.