Abstract

Representing images and videos with Symmetric Positive Definite (SPD) matrices and considering the Riemannian geometry of the resulting space has proven beneficial for many recognition tasks. Un- fortunately, computation on the Riemannian manifold of SPD matrices –especially of high-dimensional ones– comes at a high cost that lim- its the applicability of existing techniques. In this paper we introduce an approach that lets us handle high-dimensional SPD matrices by con- structing a lower-dimensional, more discriminative SPD manifold. To this end, we model the mapping from the high-dimensional SPD manifold to the low-dimensional one with an orthonormal pro jection. In particular, we search for a pro jection that yields a low-dimensional manifold with maximum discriminative power encoded via an affinity-weighted simi- larity measure based on metrics on the manifold. Learning can then be expressed as an optimization problem on a Grassmann manifold. Our evaluation on several classification tasks shows that our approach leads to a significant accuracy gain over state-of-the-art methods.