Finite mixtures of matrix normal distributions for classifying three-way data

Matrix-variate distributions represent a natural way for modeling random matrices. Realizations from random matrices are generated by the simultaneous observation of variables in different situations or locations, and are commonly arranged in three-way data structures. Among the matrix-variate distributions, the matrix normal density plays the same pivotal role as the multivariate normal distribution in the family of multivariate distributions. In this work we define and explore finite mixtures of matrix normals. An EM algorithm for the model estimation is developed and some useful properties are demonstrated. We finally show that the proposed mixture model can be a powerful tool for classifying three-way data both in supervised and unsupervised problems. A simulation study and some real examples are presented.