Locally adaptive sparse representation on Riemannian manifolds for robust classification.

With its promising classification performance, the sparse representation based classification (SRC) has attracted great attention in recent years. However, the existing SRC type methods can be only applied to vectorial data in Euclidean space. This leaves the gap for a satisfactory approach to conduct classification task for manifold-valued data such as symmetric positive definite (SPD) matrices, which are widely seen in computer vision. To address this problem, this paper proposes a locally adaptive SRC method on the SPD Riemannian manifold by using the Log-Euclidean kernel to embed the SPD matrices into a Reproducing Kernel Hilbert Space (RKHS), where the meaningful linear reconstruction of SPD matrices can be implemented. Furthermore, through exploiting the geodesic distance between SPD matrices, the proposed method can effectively characterize the intrinsic local Riemannian geometry within data so as to well uncover the underlying sub-manifold structure. Experimental results on several famous databases demonstrate that the proposed method achieves better classification results than the state-of-the-art approaches.