Compact and Understandable Descriptions of Mixtures of Bernoulli Distributions

Finite mixture models can be used in estimating complex, unknown probability distributions and also in clustering data. The parameters of the models form a complex representation and are not suitable for interpretation purposes as such. In this paper, we present a methodology to describe the finite mixture of multivariate Bernoulli distributions with a compact and understandable description. First, we cluster the data with the mixture model and subsequently extract the maximal frequent itemsets from the cluster-specific data sets. The mixture model is used to model the data set globally and the frequent itemsets model the marginal distributions of the partitioned data locally. We present the results in understandable terms that reflect the domain properties of the data. In our application of analyzing DNA copy number amplifications, the descriptions of amplification patterns are represented in nomenclature used in literature to report amplification patterns and generally used by domain experts in biology and medicine.