Kernel Sparse Subspace Clustering on Symmetric Positive Definite Manifolds

Sparse subspace clustering (SSC), as one of the most successful subspace clustering methods, has achieved notable clustering accuracy in computer vision tasks. However, SSC applies only to vector data in Euclidean space. Unfortunately there is still no satisfactory approach to solve subspace clustering by self-expressive principle for symmetric positive definite (SPD) matrices which is very useful in computer vision. In this paper, by embedding the SPD matrices into a Reproducing Kernel Hilbert Space (RKHS), a kernel subspace clustering method is constructed on the SPD manifold through an appropriate Log-Euclidean kernel, termed as kernel sparse subspace clustering on the SPD Riemannian manifold(KSSCR). By exploiting the intrinsic Riemannian geometry within data, KSSCR can effectively characterize the geodesic distance between SPD matrices to uncover the underlying subspace structure. Experimental results on several famous datasets demonstrate that the proposed method achieves better clustering results than the state-of-the-art approaches.