Kernel Sparse Subspace Clustering on Symmetric Positive Definite Manifolds
This addresses a gap in subspace clustering for SPD matrices, which are useful in computer vision, but the approach is incremental as it adapts existing sparse subspace clustering principles to a new data type.
The paper tackles subspace clustering for symmetric positive definite matrices, which lack effective methods, by proposing a kernel-based approach that embeds them into a Reproducing Kernel Hilbert Space using a Log-Euclidean kernel, achieving better clustering results than state-of-the-art methods on two databases.
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.