A Novel Algorithm for Clustering of Data on the Unit Sphere via Mixture Models

• Activity Number: 649 - Advances in Finite Mixture Modeling and Model-Based Clustering
• Type: Topic Contributed
• Date/Time: Thursday, August 3, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Hien Nguyen*
• Companies: LA TROBE UNIVERSITY
• Keywords: Finite mixture model ; Kent distribution ; Model-based clustering ; Spherical data analysis ; Stiefel Manifold

Abstract

A new maximum approximate likelihood (ML) estimation algorithm for the mixture of Kent distribution is proposed. The new algorithm is constructed via the BSLM (block successive lower-bound maximization) framework and incorporates manifold optimization procedures within it. The BSLM algorithm is iterative and monotonically increases the approximate log-likelihood function in each step. Under mild regularity conditions, the BSLM algorithm is proved to be convergent and the approximate ML estimator is proved to be consistent. A Bayesian information criterion-like (BIC-like) model selection criterion is also derive, for the task of choosing the number of components in the mixture distribution. The approximate ML estimator and the BIC-like criterion are both demonstrated to be successful via simulation studies. A model-based clustering rule is proposed and also assessed favorably via simulations. Example applications of the developed methodology are provided via an image segmentation task and a neural imaging clustering problem.