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

Abstract

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.

Keywords:

• Bayesian inference
• clustering
• DNA microarray data
• finite mixture model
• high-dimensional data
• variable selection

Acknowledgments

The authors thank the Editor, Associate Editor, and Referees for reviewing the manuscript and providing valuable comments. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.2018R1C1B6004511).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) [grant number 2018R1C1B6004511].