A macro-DAG structure based mixture model

Abstract

h i g h l i g h t s• 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. a b s t r a c tIn 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 EMmDAG, 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.

Model-based clustering with sparse covariance matrices

“…Within the context of clustering and Gaussian mixture models, seminal work can be found in Thiesson et al (1997), where the authors parameterize each component density in terms of conditional distributions and a related directed acyclic graph (DAG, Whittaker, 1990). Recent work on mixtures of DAGs is in Chalmond (2015). Rodríguez et al (2011) and Talluri et al (2014) develop a Bayesian framework for estimating infinite mixtures of sparse Gaussian graphical models where different prior distributions on the inverse covariance are employed.…”