On Parsimonious Modelling via Matrix-variate t Mixtures

Mixture models for matrix-variate data have becoming more and more popular in the most recent years. One issue of these models is the potentially high number of parameters. To address this concern, parsimonious mixtures of matrix-variate normal distributions have been recently introduced in the literature. However, when data contains groups of observations with longer-than-normal tails or atypical observations, the use of the matrix-variate normal distribution for the mixture components may affect the fitting of the resulting model. Therefore, we consider a more robust approach based on the matrix-variate t distribution for modeling the mixture components. To introduce parsimony, we use the eigen-decomposition of the components scale matrices and we allow the degrees of freedom to be equal across groups. This produces a family of 196 parsimonious matrix-variate t mixture models. Parameter estimation is obtained by using an AECM algorithm. The use of our parsimonious models is illustrated via a real data application, where parsimonious matrix-variate normal mixtures are also fitted for comparison purposes.