A macro-DAG structure based mixture model

• A two-level DAG structure is proposed for modeling multidimensional mixture.
• Unsupervised classification is revisited for this two-level DAG structure.
• A dedicated EM algorithm, called EM-mDAG, is described.
• This algorithm favors the selection of a small number of classes.
• This method provides a help for semantic interpretation of the classes.

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. This 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. This approach has two main advantages. It favors the selection of a small number of classes and it allows a semantic interpretation of the classes based on a clustering within the macro-variables.