On parsimonious models for modeling matrix data

Abstract Finite mixture modeling is a popular technique for capturing heterogeneity in data. Although the vast majority of the theory developed in this area up to date deals with vector-valued data, some recent advancements have been made to expand the concept to matrix-valued data, for example, by means of matrix Gaussian mixture models. Unfortunately, matrix mixtures tend to suffer from the overparameterization issue due to a high number of parameters involved in the model. As a result, this may lead to problems such as overfitting and mixture order underestimation. One possible approach of addressing the overparameterization issue that has proven to be effective in the vector-valued framework is to consider various parsimonious models. One of the most popular classes of parsimonious models is based on the spectral decomposition of covariance matrices. An attempt to generalize this class and make it applicable in the matrix setting is made. Estimation procedures are thoroughly discussed for all models considered. The application of the proposed methodology is studied on synthetic and real-life data sets.