On the Use of the Matrix-Variate Tail-Inflated Normal Distribution for Parsimonious Mixture Modeling

Recent advances in the matrix-variate model-based clustering literature have shown the growing interest for this kind of data modelization. In this framework, finite mixture models constitute a powerful clustering technique, despite the fact that they tend to suffer from overparameterization problems because of the high number of parameters to be estimated. To cope with this issue, parsimonious matrix-variate normal mixtures have been recently proposed in the literature. However, for many real phenomena, the tails of the mixture components of such models are lighter than required, with a direct effect on the corresponding fitting results. Thus, in this paper we introduce a family of 196 parsimonious mixture models based on the matrix-variate tail-inflated normal distribution, an elliptical heavy-tailed generalization of the matrix-variate normal distribution. Parsimony is reached by applying the well-known eigen-decomposition of the component scale matrices, as well as by allowing the tailedness parameters of the mixture components to be tied across groups. An AECM algorithm for parameter estimation is presented. The proposed models are then fitted to simulated and real data. Comparisons with parsimonious matrix-variate normal mixtures are also provided.