A Family of Parsimonious Matrix-Variate Mixture Models for Heavy-Tailed Data

Matrix-variate mixtures are the state of the art for clustering random matrices. For many real data, the conventional normality assumption for the distribution of the mixture components is often violated by the presence of heavy-tailed clusters. Additionally, a serious problem related to the matrix-variate mixtures is the potentially high number of parameters to be estimated. To jointly account for both aspects, in this work, we propose a family of parsimonious mixture models based on the matrix-variate symmetric normal mean-variance Birnbaum-Saunders distribution. Such distribution has been recently introduced in the literature and, because of its greater flexibility, allows for better modeling of data having nonnormal behavior in the tails. Parsimony is attained by employing the eigen-decomposition to the component scale matrices and by linking the tailedness parameters of mixture components across groups. An expectation conditional maximization (ECM) algorithm is outlined for maximum likelihood parameter estimation. The models are first fitted to synthetic data and then to a real dataset where the differences over other approaches are investigated.