DeepAI AI Chat
Log In Sign Up

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

by   Hien D. Nguyen, et al.

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.


page 16

page 17


Factorized Asymptotic Bayesian Hidden Markov Models

This paper addresses the issue of model selection for hidden Markov mode...

Law of the Iterated Logarithm and Model Selection Consistency for Independent and Dependent GLMs

We study the law of the iterated logarithm (LIL) for the maximum likelih...

An Introduction to the Practical and Theoretical Aspects of Mixture-of-Experts Modeling

Mixture-of-experts (MoE) models are a powerful paradigm for modeling of ...

Block-wise Minimization-Majorization algorithm for Huber's criterion: sparse learning and applications

Huber's criterion can be used for robust joint estimation of regression ...

Conjugate Mixture Models for Clustering Multimodal Data

The problem of multimodal clustering arises whenever the data are gather...

Maximum weighted likelihood estimator for robust heavy-tail modelling of finite mixture models

In this article, we present the maximum weighted likelihood estimator (M...

Clustering of count data through a mixture of multinomial PCA

Count data is becoming more and more ubiquitous in a wide range of appli...