Count Data Clustering using Unsupervised Localized Feature Selection and Outliers Rejection

This paper presents an unsupervised statistical model for simultaneous clustering, feature selection and outlier rejection in the case of count data. The proposed model is based on a finite discrete mixture to which a uniform component is added to ensure robustness to outliers and noise. The consideration of a finite mixture model is justified by its flexibility, its solid grounding in the theory of statistics and its competitive results. We derive a complete maximum a posteriori learning approach that does not require a priori knowledge about the number of outliers and the number of clusters. A rigorous expectation maximization (EM) algorithm, based on the formulation of a maximum a posteriori (MAP) estimation, is also provided. We report experimental results of applying our model to the challenging problems of visual scenes categorization and texture discrimination.