Dirichlet process mixture models on symmetric positive definite matrices for appearance clustering in video surveillance applications

Covariance matrices of multivariate data capture feature correlations compactly, and being very robust to noise, they have been used extensively as feature descriptors in many areas in computer vision, like, people appearance tracking, DTI imaging, face recognition, etc. Since these matrices do not adhere to the Euclidean geometry, clustering algorithms using the traditional distance measures cannot be directly extended to them. Prior work in this area has been restricted to using K-means type clustering over the Rieman-nian space using the Riemannian metric. As the applications scale, it is not practical to assume the number of components in a clustering model, failing any soft-clustering algorithm. In this paper, a novel application of the Dirich-let Process Mixture Model framework is proposed towards unsupervised clustering of symmetric positive definite matrices. We approach the problem by extending the existing K-means type clustering algorithms based on the logdet divergence measure and derive the counterpart of it in a Bayesian framework, which leads to the Wishart-Inverse Wishart conjugate pair. Alternative possibilities based on the matrix Frobenius norm and log-Euclidean measures are also proposed. The models are extensively compared using two real-world datasets against the state-of-the-art algorithms and demonstrate superior performance.