A Novel Algorithm for Clustering of Data on the Unit Sphere via Mixture Models
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.
Cite
@article{arxiv.1709.04611,
title = {A Novel Algorithm for Clustering of Data on the Unit Sphere via Mixture Models},
author = {Hien D. Nguyen},
journal= {arXiv preprint arXiv:1709.04611},
year = {2017}
}