Bayesian sparse convex clustering via global-local shrinkage priors

TL;DR

This paper introduces a Bayesian approach to sparse convex clustering that improves variable selection and clustering accuracy by using global-local shrinkage priors, with demonstrated effectiveness through simulations and real data.

Contribution

It proposes a novel Bayesian sparse convex clustering method utilizing global-local shrinkage priors, enhancing estimation accuracy over traditional L1 regularization.

Findings

Effective in simulation studies

Demonstrated on real data

Improves variable selection accuracy

Abstract

Sparse convex clustering is to cluster observations and conduct variable selection simultaneously in the framework of convex clustering. Although a weighted $L_1$ norm is usually employed for the regularization term in sparse convex clustering, its use increases the dependence on the data and reduces the estimation accuracy if the sample size is not sufficient. To tackle these problems, this paper proposes a Bayesian sparse convex clustering method based on the ideas of Bayesian lasso and global-local shrinkage priors. We introduce Gibbs sampling algorithms for our method using scale mixtures of normal distributions. The effectiveness of the proposed methods is shown in simulation studies and a real data analysis.