Bayesian variable selection in clustering high-dimensional data via a mixture of finite mixtures

When clustering high-dimensional data, it is often important to identify variables that discriminate the clusters. Meanwhile, a common issue in clustering is to determine the number of clusters. In this study, we propose a new method that simultaneously performs clustering and variable selection, while inferring the number of clusters from the data. We formulate the clustering problem using a finite mixture model with a symmetric Dirichlet weights prior, while also placing a prior on the number of components. That is, we utilize a mixture of finite mixtures. We handle the variable selection problem by introducing a latent binary vector, which represents the inclusion/exclusion of variables. We update the binary vector for variable selection using a Metropolis algorithm and perform inference on the cluster structure using a split-merge Markov chain Monte Carlo technique. We demonstrate the advantage of our method using simulated and two real DNA microarray datasets.