Model-based clustering, classification, and discriminant analysis via mixtures of multivariate /-distributions

摘要

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 covari-ance matrices to give families of mixture models. Similar approaches have also been applied, albeit with less fecun-dity, to classification and discriminant analysis. In this pa-per, 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 com-ponent is modeled using a multivariate r-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 fam-ily for clustering, classification, and discriminant analysis is illustrated with both real and simulated data. The perfor-mance of this family is compared to its Gaussian counterpart on three real data sets.