Multi-kernel sparse subspace clustering on the Riemannian manifold of symmetric positive definite matrices

Abstract

Recently, clustering in the Riemannian manifolds has received a great interest. The main specificity of this kind of spaces is their ability to detect nonlinear forms in the real world data groups. Accordingly, numerous Euclidean clustering algorithms have been emerged to the Riemannian framework. One of them is the Sparse Subspace Clustering (SSC) method. Within this context, an interesting method named Kernel Sparse Subspace Clustering in the Riemannian manifold (KSSCR) has been proposed. In order to improve the clustering performance of the SSC method, KSSCR is based on the idea of data projection into a Reproducing Kernel Hilbert Space (RKHS) through a Riemannian kernel. This modification in terms of projection space has yielded to significant clustering results compared to the original SSC. This paper proposed a Multi-Kernel SSCR (MKSSCR) method. The idea is to create a linear combination of a set of Riemannian kernels. In fact, by using a single kernel, the faraway points will be neglected. Thus, the key motivation of this work is to use a mixture of kernels. The purpose here is to emphasis the closest data points without ignoring the faraway ones in the process of selecting neighbors for each data point. Several experiments carried out on varied face clustering data sets demonstrate the clustering accuracy improvement by the proposed method compared to other state-of-the-art methods.