Mixtures of Matrix Variate Bilinear Factor Analyzers

Dimensionality is an ever present concern with data becoming increasingly higher dimensional over the last few years. To combat this issue, dimension reduction techniques have become very important tools, especially in the area of clustering (unsupervised classification) as well as semi-supervised and supervised classification. For multivariate data, the mixture of factor analyzers model has proved to be very useful in this regard as the model performs clustering and dimension reduction simultaneously, details in Section 2. However, there is 1 relative paucity in the area of dimension reduction for use in model-based clustering for matrix variate data. Matrix variate distributions have been shown to be useful for modelling three way data such as images and multivariate longitudinal data; however, the methods presented in the literature do suffer from dimensionality concerns. In this paper, we present a mixture of matrix variate bilinear factor analyzers (MMVBFA) model for use in clustering for higher dimensional matrix data. The matrix variate bilinear factor analyzers model can be viewed as a generalization of bilinear principal component analysis (BPCA; Zhao et al. 2012), and contains BPCA as a special case. An alternating expectation conditional maximization (AECM) algorithm (Meng & van Dyk 1997) is used for parameter estimation. The proposed method is illustrated using both simulated and real datasets.