  Over the years data has 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. Although dimension reduction in
the area of clustering for multivariate data has been quite thoroughly
discussed within the literature, there is relatively little work in the area of
three-way, or matrix variate, data. Herein, we develop a mixture of matrix
variate bilinear factor analyzers (MMVBFA) model for use in clustering
high-dimensional matrix variate data. This work can be considered both the
first matrix variate bilinear factor analysis model as well as the first MMVBFA
model. Parameter estimation is discussed, and the MMVBFA model is illustrated
using simulated and real data.
