Abstract

Recent advances suggest that a wide range of computer vision prob- lems can be addressed more appropriately by considering non-Euclidean geome- try. This paper tackles the problem of sparse coding and dictionary learning in the space of symmetric positive definite matrices, which form a Riemannian mani- fold. With the aid of the recently introduced Stein kernel (related to a symmetric version of Bregman matrix divergence), we propose to perform sparse coding by embedding Riemannian manifolds into reproducing kernel Hilbert spaces. This leads to a convex and kernel version of the Lasso problem, which can be solved efficiently. We furthermore propose an algorithm for learning a Riemannian dic- tionary (used for sparse coding), closely tied to the Stein kernel. Experiments on several classi fication tasks (face recognition, texture classi fication, person re- identi fication) show that the proposed sparse coding approach achieves notable improvements in discrimination accuracy, in comparison to state-of-the-art meth- ods such as tensor sparse coding, Riemannian locality preserving projection, and symmetry-driven accumulation of local features.