Dirichlet process mixture models for time-dependent clustering

Abstract

In many problems of signal processing, an important task is the classification of data. A group of methods that has attracted much interest for this purpose are the nonparametric Bayesian methods, and in particular, those based on the Dirichlet process. A useful metaphor for various generalizations of the Dirichlet process has been the Chinese restaurant process. Often the task of classification must be carried out in a sequential manner, and to that end the concepts from Bayesian non-parametrics cannot be applied straightforwardly. Recently, we introduced the notion of Chinese restaurant process with finite capacity to allow for classification of data on a time-varying basis. In this paper, we introduce the hierarchical Chinese restaurant process with finite capacity to provide further flexibilities to the process of classification. We show a generative model based on the process and then describe how to make online inference using the model. We demonstrate the approach with computer simulations.