Riemannian Manifolds clustering via Geometric median

In this paper, we propose a new kernel function that makes use of Riemannian geodesic distance s among data points, and present a Geometric median shift algorithm over Riemannian Manifolds. Relying on the geometric median shift, together with geodesic distances, our approach is able to effectively cluster data points distributed on Riemannian manifolds. In addition to improving the clustering results, Using both Riemannian Manifolds and Euclidean spaces, We compare the geometric median shift and mean shift algorithms on synthetic and real data sets for the tasks of clustering.