Nonparametric Hierarchical Bayesian Models for Positive Data Clustering Based on Inverted Dirichlet-Based Distributions

In this paper, we propose nonparametric hierarchical Bayesian models based on two inverted Dirichlet-based distributions and Pitman-Yor process for positive data features clustering. The choice of the inverted Dirichlet and the generalized inverted Dirichlet distributions is motivated by their flexibility and modeling capabilities when dealing with this kind of data, while deploying the Pitman-Yor process prior is justified by its power-law behavior, which makes it a natural choice in real-life application compared with Dirichlet processes for instance. The inference for the resulting models takes into account the challenging problem of feature weighting/selection and is conducted under a Bayesian setting by means of the recently proposed stochastic variational Bayes technique. The efficacy and merits of the proposed approaches are examined using the synthetic data and a challenging real-life application that concerns video background subtraction.