Mixtures of Skewed Matrix Variate Bilinear Factor Analyzers

TL;DR

This paper introduces four new mixture models for matrix variate data that incorporate skewed distributions, addressing the limitations of normality assumptions in high-dimensional clustering tasks.

Contribution

It proposes novel mixtures of bilinear factor analyzers using skewed matrix variate distributions, expanding clustering methods beyond normality assumptions.

Findings

Four new mixture models based on skewed distributions

Enhanced clustering capability for skewed matrix variate data

Addresses limitations of existing normality-based methods

Abstract

In recent years, data have become increasingly higher dimensional and, therefore, an increased need has arisen for dimension reduction techniques for clustering. Although such techniques are firmly established in the literature for multivariate data, there is a relative paucity in the area of matrix variate, or three-way, data. Furthermore, the few methods that are available all assume matrix variate normality, which is not always sensible if cluster skewness or excess kurtosis is present. Mixtures of bilinear factor analyzers using skewed matrix variate distributions are proposed. In all, four such mixture models are presented, based on matrix variate skew-t, generalized hyperbolic, variance-gamma, and normal inverse Gaussian distributions, respectively.