  Many applications of interest involve data that can be analyzed as unit
vectors on a d-dimensional sphere. Specific examples include text mining, in
particular clustering of documents, biology, astronomy and medicine among
others. Previous work has proposed a clustering method using mixtures of
Poisson kernel-based distributions (PKBD) on the sphere. We prove
identifiability of mixtures of the aforementioned model, convergence of the
associated EM-type algorithm and study its operational characteristics.
Furthermore, we propose an empirical densities distance plot for estimating the
number of clusters in a PKBD model. Finally, we propose a method to simulate
data from Poisson kernel-based densities and exemplify our methods via
application on real data sets and simulation experiments.
