A Bayesian Mixture Model for Clustering on the Stiefel Manifold

TL;DR

This paper introduces a Bayesian mixture model for clustering on the Stiefel manifold using the Matrix Langevin distribution, featuring novel conjugate priors and an efficient MCMC sampling scheme, validated through simulations and real-world neuroimaging data.

Contribution

It develops a new Bayesian mixture model with conjugate priors for the Matrix Langevin distribution on the Stiefel manifold, along with an efficient MCMC sampling algorithm.

Findings

Model achieves accurate clustering in simulations

Method demonstrates computational efficiency on large datasets

Real-world neuroimaging data analysis confirms practical applicability

Abstract

Analysis of a Bayesian mixture model for the Matrix Langevin distribution on the Stiefel manifold is presented. The model exploits a particular parametrization of the Matrix Langevin distribution, various aspects of which are elaborated on. A general, and novel, family of conjugate priors, and an efficient Markov chain Monte Carlo (MCMC) sampling scheme for the corresponding posteriors is then developed for the mixture model. Theoretical properties of the prior and posterior distributions, including posterior consistency, are explored in detail. Extensive simulation experiments are presented to validate the efficacy of the framework. Real-world examples, including a large scale neuroimaging dataset, are analyzed to demonstrate the computational tractability of the approach.