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

• Activity Number: 588 - Statistical Learning: Clustering
• Type: Contributed
• Date/Time: Wednesday, August 2, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Mojgan Golzy* and Marianthi Markatou and Alexander Foss
• Companies: State University of New York At Buffalo and University at buffalo, Department of Biostatistics and State University of New York at Buffalo
• Keywords: Clustering ; Directional data ; Mixture models ; Poisson kernel

Abstract

In many applications, such as medical text categorization, gene expression profiling or understanding the microstructure property relations of materials the direction of the data vectors is more important than their magnitude. Natural models for this type of data are von Mises-Fisher (vMF) distribution, inverse stereographic projections of multivariate normal & Watson distributions. However, there is no close expression for the estimate of some parameters in these models. We present a clustering method based on mixtures of Poisson kernel based distributions on the sphere. We derive the estimates of the parameters, describe the corresponding clustering algorithm and prove its convergence. We investigate the data structure characteristics that facilitate superior performance of our algorithm. Our primary experimental results show that Poisson kernel based clustering has superior performance in the presence of noisy data than the state of the art mixture of von Mises-Fisher distributions. Finally, we describe an algorithm for generating high-dimensional directional data from the Poisson kernel based distribution for a simulation-based comparisons.