## Model-based clustering, classification, and discriminant analysis via mixtures of multivariate $$t$$-distributions.(English)Zbl 1252.62062

Summary: 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. 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 $$t$$EIGEN 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.

### MSC:

 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62H10 Multivariate distribution of statistics 65C60 Computational problems in statistics (MSC2010)

### Software:

R; PGMM; mclust; S-PLUS
Full Text:

### References:

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