Extension of the mixture of factor analyzers model to incorporate the multivariate t-distribution

Authors:
G. J. McLachlan;R. W. Bean;L. Ben-Tovim Jones
Affiliations:
Department of Mathematics and the Institute for Molecular Bioscience, University of Queensland, St. Lucia, Brisbane 4072, Australia;Department of Mathematics and the Institute for Molecular Bioscience, University of Queensland, St. Lucia, Brisbane 4072, Australia;Department of Mathematics and the Institute for Molecular Bioscience, University of Queensland, St. Lucia, Brisbane 4072, Australia
Venue:
Computational Statistics & Data Analysis
Year:
2007

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Abstract

Mixtures of factor analyzers enable model-based density estimation to be undertaken for high-dimensional data, where the number of observations n is small relative to their dimension p. However, this approach is sensitive to outliers as it is based on a mixture model in which the multivariate normal family of distributions is assumed for the component error and factor distributions. An extension to mixtures of t-factor analyzers is considered, whereby the multivariate t-family is adopted for the component error and factor distributions. An EM-based algorithm is developed for the fitting of mixtures of t-factor analyzers. Its application is demonstrated in the clustering of some microarray gene-expression data.