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

Multivariate spatio-temporal data arise from the observation of a set ofmeasurements in different times on a sample of spatially correlated locations. Theycan be arranged in a three-way data structure characterized by rows, columns andlayers. In this perspective each observed statistical unit is a matrix of observationsinstead of the conventional p-dimensional vector. In this work we propose modelbased clustering for this wide class of continuous three-way data by a general mixturemodel with components modelled by matrix-variate Gaussian distributions. Theeffectiveness of the proposed method is illustrated on multivariate crime data collectedon the Italian provinces in the years 2005-2009.