  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. As such,
there is still no satisfactory approach to solve subspace clustering by ${\it
self-expressive}$ 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 two famous database demonstrate that the proposed method achieves better
clustering results than the state-of-the-art approaches.
