Crossed clustering: methods and models

The relations between automatic clustering methods and inferential statistical models have mostly been studied when the data involve only one set. We propose to study these relations in the case of data involving two sets. We shall look at cross clustering methods as suggested by Govaert; we show that these methods, like the simple clustering methods, can be considered as a clustering approach of a mixture model. We introduce the notion of crossed mixture from a concrete example and define the notions of likelihood and associated clustered likelihood. Then, we study the relations which exist between the crossed mixture models and simple models and we show that these relations are completely similar to those which exist between the crossed clustering methods and simple clustering methods.