Parsimonious Mixtures of Matrix Variate Bilinear Factor Analyzers

Over the years, data have become increasingly higher dimensional, which has prompted an increased need for dimension reduction techniques. This is perhaps especially true for clustering (unsupervised classification), as well as semi-supervised and supervised classification. Many methods have been proposed in the literature for two-way (multivariate) data and quite recently methods have been presented for three-way (matrix variate) data. One such method is the mixtures of matrix variate bilinear factor analyzers (MMVBFA) model. Herein, we propose a total of 64 parsimonious MMVBFA models. Simulated and real data are used for illustration.