Algorithms for clustering on the sphere: Advances & applications

Model-based clustering of directional data has been proposed as a basis for clustering by many authors, using mixtures of different distributions that are natural for directional data such as von Mises-Fisher (vMF) distribution, and Watson distribution. However, when vMF and Watson distributions are used as component densities, an approximation of the concentration parameter is used to estimate k in both cases. We present a clustering method based on mixtures of Poisson kernels on the sphere. The Poisson kernel offers a natural way of clustering data on the surface of a sphere as well as in the ball and half-sphere. We derive estimates of the parameters and describe the corresponding clustering algorithm. We compare the performance of this model with existing methods.