Robust classification via finite mixtures of matrix-variate skew t distributions

TL;DR

This paper introduces the matrix-variate skew t distribution (MVST) for flexible modeling of asymmetric matrix-variate data, develops an EM algorithm for parameter estimation, and demonstrates its effectiveness through simulations and real data applications.

Contribution

The paper proposes the novel MVST distribution and an EM algorithm for its parameters, extending mixture models to better handle skewed matrix-variate data.

Findings

MVST effectively models asymmetric matrix-variate data

The EM algorithm provides accurate maximum likelihood estimates

Empirical results confirm improved clustering performance

Abstract

Analysis of matrix-variate data is becoming increasingly common in the literature, particularly in the field of clustering and classification. It is well-known that real data, including real matrix-variate data, often exhibit high levels of asymmetry. To address this issue, one common approach is to introduce a tail or skewness parameter to a symmetric distribution. In this regard, we introduced here a new distribution called the matrix-variate skew t distribution (MVST), which provides flexibility in terms of heavy tail and skewness. We then conduct a thorough investigation of various characterizations and probabilistic properties of the MVST distribution. We also explore extensions of this distribution to a finite mixture model. To estimate the parameters of the MVST distribution, we develop an efficient EM-type algorithm that computes maximum likelihood (ML) estimates of the model parameters. To validate the effectiveness and usefulness of the developed models and associated methods, we perform empirical experiments using simulated data as well as three real data examples. Our results demonstrate the efficacy of the developed approach in handling asymmetric matrix-variate data.