6.  L ₂ Normalized Data Clustering Through the Dirichlet Process Mixture Model of von Mises Distributions with Localized Feature Selection

In this chapter, we propose a probabilistic model based-approach for clustering L ₂ normalized data. Our approach is based on the Dirichlet process mixture model of von Mises (VM) distributions. Since it assumes an infinite number of clusters (i.e., the mixture components), the Dirichlet process mixture model of VM distributions can also be considered as the infinite VM mixture model. Comparing with finite mixture model in which the number of mixture components have to be determined through extra efforts, the infinite mixture VM model is a nonparametric model such that the number of mixture components is assumed to be infinite initially and will be inferred automatically during the learning process. To improve clustering performance for high-dimensional data, a localized feature selection scheme is integrated into the infinite VM mixture model which can effectively detect irrelevant features based on the estimated feature saliencies. In order to learn the proposed infinite mixture model with localized feature selection, we develop an effective approach using variational inference that can estimate model parameters and feature saliencies with closed-form solutions. Our model-based clustering approach is validated through two challenging applications, namely topic novelty detection and unsupervised image categorization.