Hierarchical Dirichlet and Pitman–Yor process mixtures of shifted‐scaled Dirichlet distributions for proportional data modeling

Abstract

In this article, first, we propose a novel unsupervised learning method based on a hierarchical Dirichlet process mixture of shifted-scaled Dirichlet (SSD) distributions. Second, we extend it to a hierarchical Pitman-Yor process mixture of SSD distributions. The goal is to find a model that properly fits complex real-world data. Our models are based on SSD distributions that are more flexible than Dirichlet distribution in fitting proportional data. Simultaneous data fitting (parameter estimate) and model selection (model complexity determination) are possible with the suggested methods. We applied batch and online variational inference for learning the models. The online setting allows us to feed our models with large-scale streaming data. The effectiveness of our proposed models is evaluated by four realistic and challenging applications, namely, spam email detection, texture clustering, traffic sign detection, and vehicle detection.Experimental results demonstrate the potential of our models to fit proportional data.