Metric learning for semi-supervised clustering of region covariance descriptors

in this paper we extend distance metric learning to a new class of descriptors known as Region Covariance Descriptors. Region covariances are becoming increasingly popular as features for object detection and classification over the past few years. Given a set of pairwise constraints by the user, we want to perform semi-supervised clustering of these descriptors aided by metric learning approaches. The covariance descriptors belong to the special class of symmetric positive definite (SPD) tensors, and current algorithms cannot deal with them directly without violating their positive definiteness. In our framework, the distance metric on the manifold of SPD matrices is represented as an L₂ distance in a vector space, and a Mahalanobis-type distance metric is learnt in the new space, in order to improve the performance of semi-supervised clustering of region covariances. We present results from clustering of covariance descriptors representing different human images, from single and multiple camera views. This transformation from a set of positive definite tensors to a Euclidean space paves the way for the application of many other vector-space methods to this class of descriptors.