Cross clustering and models

The relations between automatic clustering methods and inferentiel statisti cal models have mostely been studied when the data involves only one set. W e propose to study these relations in the case of data involving two sets. We shall look at cross clustering methods as suggested by Govaert [6]; we s how that these methods, like the simple clustering methods, can be consider ed as a clustering approach of a mixture model. We introduce the notion of crossed mixture from a concret example and define the notions of likelihood and associated clustered likelihood Then, wt study the relations which exi st between the crossed mixture models and simple models and we show that th ese relations are completely similar to those which exist between the cross ed clustering methods and simple clustering methods.