Parsimonious Mixtures of Matrix-Variate Shifted Exponential Normal Distributions

Finite mixtures of matrix-variate distributions constitute a powerful model-based clustering device. One serious issue of these models is the potentially high number of parameters to be estimated. Thus, in this work we introduce a family of 196 parsimonious mixture models based on the matrix-variate shifted exponential normal distribution, an elliptical heavy-tailed generalization of the matrix-variate normal distribution. Parsimony is introduced in a twofold manner: (i) by using the eigendecomposition of the components scale matrices and (ii) by allowing the components tailedness parameter to be tied across the groups. A further characteristic of the proposed models relies on the more flexible tail behavior with respect to existing parsimonious matrix-variate normal mixtures, thus allowing for a better modeling of datasets having atypical observations. Parameter estimation is obtained by using an ECM algorithm. The proposed models are then fitted to a real dataset along with parsimonious matrix-variate normal mixtures for comparison purposes.