Clustering on the d-Dimensional Sphere: Latest Trends and the Role of Poisson Kernel-Based Density Models

Scientific work produces many data sets that can be analyzed as unit vectors on a d-dimensional sphere. Specific examples include clustering of documents, the study of comets, and data that arise in the analysis of microarray experiments where interest centers in identifying groups of genes that are functionally related. We offer a succinct review of the literature on clustering on the d-dimensional sphere. We then discuss the role that Poisson kernel-based density models play in clustering, highlighting their connection with the Brownian motion and other classes of densities. A special class of kernels, called diffusion kernels, is also discussed. Software for the use of a clustering method based on mixtures of Poisson kernel-based densities is also reviewed.