Expectation propagation learning of a Dirichlet process mixture of Beta-Liouville distributions for proportional data clustering

• A statistical model based on a Dirichlet process mixture of Beta-Liouville distributions is proposed.
• An expectation propagation framework is developed to learn the parameters of the proposed model.
• The approach is investigated via facial expression and action recognition.

We propose a nonparametric Bayesian model for the clustering of proportional data. Our model is based on an infinite mixture of Beta-Liouville distributions and allows a compact description of complex data. The choice of the Beta-Liouville as the basis of our model is justified by the fact that it has been shown to be a good alternative to the Dirichlet and generalized Dirichlet distributions for the statistical representation of proportional data. Using this infinite mixture, we show how a careful modeling can achieve good results by allowing the elicitation of prior belief about the parameters and the number of clusters through suitable learning. Indeed, we develop an efficient learning algorithm, based on expectation propagation, to estimate the parameters of our infinite Beta-Liouville mixture model. The feasibility and effectiveness of the proposed method are demonstrated by two challenging applications namely action and facial expression recognition.