Abstract
Recently, there has been an increasing interest in developing tools able to find groups in matrix-valued data. To this extent, matrix Gaussian mixture models (MGMM) represent an extension of the popular model-based clustering based on normal mixtures. Unfortunately overparametrization issues, already affecting the vector-variate framework, are exacerbated in the MGMM one, where the number of parameters grows quadratically with both row and column dimensions. To overcome this limitation, we introduce a sparse model-based clustering approach for three-way data structures. The proposed penalized estimation scheme, shrinking the estimates towards zero, achieves more stable and parsimonious clustering in high-dimensional scenarios. An application to satellite images underlines the benefits of the proposal.