Geodesic Clustering

We propose a new class of distances for the purpose of data clustering, called the geodesic distance, and introduce a geodesic extension of K-medoids algorithm. We analyze the theoretical properties of the geodesic distance within a clustering framework and prove that the geodesic K-medoids algorithm converges to the correct clustering assignment in the asymptotic regime, even in the presence of outliers. We also present experimental evidence on the abilities of geodesic Kmedoids to handle clustering problems involving outliers, nonlinearly separable clusters, and varying densities in the clusters. The results are compared to a few hierarchical and spectral clustering algorithms on several clustering problems.