On model-based clustering of skewed matrix data

Abstract

The existing finite mixture modeling and model-based clustering literature focuses primarily on the analysis of multivariate data observed in the form of vectors, with each element representing a specific feature. In this setting, multivariate Gaussian mixture models have been the most commonly used. Due to severe modeling issues observed when normal components cannot provide adequate fit to groups, much attention has been paid to developing models capable of accounting for skewness in data. In our work, we target the problem of mixture modeling with components that can handle skewness in matrix-valued data. The proposed developments open a wide range of possible modeling capabilities, with numerous applications, as illustrated in this paper. A novel matrix mixture model is proposed. Its skewness parameters enjoy appealing interpretability. The corresponding estimation procedure and various ways of parameterization are discussed. Comprehensive simulation studies and applications to real-life datasets illustrate the efficiency of the proposed developments, supported by good results.