In the context of unsupervised classification of multidimensional data, we revisit the classical mixture model in the case where the dependencies among the random variables are described by a DAG structure. The structure is considered at two levels, the original DAG and its macro-representation. This two-level representation is the main base of the proposed mixture model. To perform unsupervised classification, we propose a dedicated algorithm called EM-mDAG, which extends the classical EM algorithm. In the Gaussian case, we show that this algorithm can be efficiently implemented. The experiments reveal that this method favors the selection of a small number of classes.
