Online Variational Learning for a Dirichlet Process Mixture of Dirichlet Distributions and Its Application

Online algorithms allow data points to be processed sequentially, which is important for real-time applications. In this paper, we propose a novel online clustering approach based on a mixture of Dirichlet processes with Dirichlet distributions, which can be viewed as an extension of the finite Dirichlet mixture model to the infinite case. Our approach is based on nonparametric Bayesian analysis, the determination of the number of clusters is sidestepped by assuming an infinite number of clusters. By learning the proposed model in an online manner with a variational learning framework, all the involved parameters can be estimated effectively and efficiently in a closed form without introducing the problem of overfitting. The proposed online infinite mixture model is validated through both synthetic data sets and a challenging real-world application namely unsupervised image categorization.