Model based clustering of multivariate spatio-temporal data: a matrix-variate approach

Multivariate spatio-temporal data arise from the observation of a set of measurements in different times on a sample of spatially correlated locations. They can be arranged in a three-way data structure characterized by rows, columns and layers. In this perspective each obseved statistical unit is a matrix of observations instead of the conventional p-dimensional vector. In this work we propose model based clustering for the wide class of continuous three-way data by a general mixture model with components modelled by matrix-variate Gaussian distributions. The effectiveness of the proposed method is illustrated on multivariate crime data collected on the Italian provinces in the years 2005-2009.