  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.
