Relational divergence based classification on Riemannian manifolds

A recent trend in computer vision is to represent images through covariance matrices, which can be treated as points on a special class of Riemannian manifolds. A popular way of analysing such manifolds is to embed them in Euclidean spaces, a process which can be interpreted as warping the feature space. Embedding manifolds is not without problems, as the manifold structure may not be accurately preserved. In this paper, we propose a new method for analysing Riemannian manifolds, where embedding into Euclidean spaces is not explicitly required. To this end, we propose to represent Riemannian points through their similarities to a set of reference points on the manifold, with the aid of the recently proposed Stein divergence, which is a symmetrised version of Bregman matrix divergence. Classification problems on manifolds are then effectively converted into the problem of finding appropriate machinery over the space of similarities, which can be tackled by conventional Euclidean learning methods such as linear discriminant analysis. Experiments on face recognition, person re-identification and texture classification show that the proposed method outperforms state-of-the-art approaches, such as Tensor Sparse Coding, Histogram Plus Epitome and the recent Riemannian Locality Preserving Projection.