Some Bayesian biclustering methods: Modeling and inference

Abstract

Standard one‐way clustering methods form homogeneous groups in a set of objects. Biclustering (or, two‐way clustering) methods simultaneously cluster rows and columns of a rectangular data array in such a way that responses are homogeneous for all row‐cluster by column‐cluster cells. We propose a Bayes methodology for biclustering and corresponding MCMC algorithms. Our method not only identifies homogeneous biclusters, but also provides posterior probabilities that particular instances or features are clustered together. We further extend our proposal to address the biclustering problem under the commonly occurring situation of incomplete datasets. In addition to identifying homogeneous sets of rows and sets of columns, as in the complete data scenario, our approach also generates plausible predictions for missing/unobserved entries in the rectangular data array. Performances of our methodology are illustrated through simulation studies and applications to real datasets.