Mixtures of Skewed Matrix Variate Bilinear Factor Analyzers

Clustering is the process of finding and analyzing underlying group structures in data. In recent years, data as become increasingly higher dimensional and therefore an increased need for dimension reduction techniques for use in 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, these few methods all assume matrix variate normality which is not always sensible if skewness is present. We propose a mixture of bilinear factor analyzers model using four skewed matrix variate distributions, namely the matrix variate skew-t, generalized hyperbolic, variance gamma and normal inverse Gaussian distributions.