Journal
STATISTICS AND COMPUTING
Volume 22, Issue 5, Pages 1021-1029Publisher
SPRINGER
DOI: 10.1007/s11222-011-9272-x
Keywords
Classification; Clustering; Discriminant analysis; Eigen-decomposition; Mixture models; Model-based clustering; Multivariate t-distribution
Funding
- Natural Sciences & Engineering Research Council of Canada
- Compusense Inc.
- Ontario Centres of Excellence
- University Research Chair in Computational Statistics at the University of Guelph
- Canada Foundation for Innovation
- Ontario Ministry for Research Innovation
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The last decade has seen an explosion of work on the use of mixture models for clustering. The use of the Gaussian mixture model has been common practice, with constraints sometimes imposed upon the component covariance matrices to give families of mixture models. Similar approaches have also been applied, albeit with less fecundity, to classification and discriminant analysis. In this paper, we begin with an introduction to model-based clustering and a succinct account of the state-of-the-art. We then put forth a novel family of mixture models wherein each component is modeled using a multivariate t-distribution with an eigen-decomposed covariance structure. This family, which is largely a t-analogue of the well-known MCLUST family, is known as the tEIGEN family. The efficacy of this family for clustering, classification, and discriminant analysis is illustrated with both real and simulated data. The performance of this family is compared to its Gaussian counterpart on three real data sets.
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