Simultaneous clustering and feature selection via nonparametric Pitman–Yor process mixture models

Abstract

Mixture models constitute one of the most important machine learning approaches. Indeed, they can be considered as the workhorse of generative machine learning. The majority of existing works consider mixtures of Gaussians. Unlike these works, this paper concentrates on nonparametric Bayesian models with Dirichlet-based mixtures. In particular, we consider the case when a Pitman–Yor process prior is adopted. Two central problems when considering such mixtures can be regarded as selecting ‘meaningful’ (or relevant) features and estimating the model’s parameters. We develop an efficient algorithm for model inference, based on the collapsed variational Bayes framework with 0th-order Taylor approximation. The merits and efficacy of the proposed nonparametric Bayesian model are demonstrated via challenging applications that concern real-world data clustering and 3D objects recognition.