Poisson Kernel-Based Clustering on the Sphere: Convergence Properties, Identifiability, and a Method of Sampling

2018/03/12 by Mojgan Golzy, Golzy, Mojgan, Marianthi Markatou +1 · 2 citations
Computer Science · #Advanced Clustering Algorithms Research #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.1803.04485

openalex publication_date 2018/03/12 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

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.

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