Consensus clustering for Bayesian mixture models

Motivation: Cluster analysis is an integral part of precision medicine and systems biology, used to define groups of patients or biomolecules. However, problems such as choosing the number of clusters and issues with high dimensional data arise consistently. An ensemble approach, such as consensus blustering, can overcome some of the difficulties associated with high dimensional data, frequently exploring more relevant clustering solutions than individual models. Another tool for cluster analysis, Bayesian mixture modelling, has alternative advantages, including the ability to infer the number of clusters present and extensibility. However, inference of these models is often performed using Markov-chain Monte Carlo (MCMC) methods which can suffer from problems such as poor exploration of the posterior distribution and long runtimes. This makes applying Bayesian mixture models and their extensions to 'omics data challenging. We apply consensus clustering to Bayesian mixture models to address these problems. Results: Consensus clustering of Bayesian mixture models successfully finds generating structure in our simulation study and captures multiple modes in the likelihood surface. This approach also offers significant reductions in runtime compared to traditional Bayesian inference when a parallel environment is available. We propose a heuristic to decide upon ensemble size and then apply consensus clustering to Multiple Dataset Integration, an extension of Bayesian mixture models for integrative analyses, on three 'omics datasets for budding yeast. We find clusters of genes that are co-expressed and have common regulatory proteins which we validate using external knowledge, showing consensus clustering can be applied to any MCMC-based clustering method.