Mixture models for simultaneous classification and reduction of three-way data

Finite mixture models are often used to classify two- (units and variables) or three- (units, variables and occasions) way data. However, two issues arise: a huge number of variables and/or occasions implies a huge number of model parameters; the existence of noise variables (and/or occasions) could mask the true cluster structure. The main aim of this paper is to reduce the number of model parameters by identifying a sub-space containing the information needed to classify the observations. This should help in identifying noise variables and/or occasions. The maximum likelihood model estimation is carried out through an EM-like algorithm. The effectiveness of the proposal is assessed through a simulation study and some applications to real data.