Abstract
Cluster analysis is an integral part of precision medicine and systems biology, used to define groups of patients or biomolecules. Consensus clustering is an ensemble approach that is widely used in these areas, which combines the output from multiple runs of a non-deterministic clustering algorithm. Here we consider the application of consensus clustering to a broad class of heuristic clustering algorithms that can be derived from Bayesian mixture models (and extensions thereof) by adopting an early stopping criterion when performing sampling-based inference for these models. While the resulting approach is non-Bayesian, it inherits the usual benefits of consensus clustering, particularly in terms of computational scalability and providing assessments of clustering stability/robustness.
In simulation studies, we show that our approach can successfully uncover the target clustering structure, while also exploring different plausible clusterings of the data. We show that, when a parallel computation environment is available, our approach offers significant reductions in runtime compared to performing sampling-based Bayesian inference for the underlying model, while retaining many of the practical benefits of the Bayesian approach, such as exploring different numbers of clusters. We propose a heuristic to decide upon ensemble size and the early stopping criterion, and then apply consensus clustering to a clustering algorithm derived from a Bayesian integrative clustering method. We use the resulting approach to perform an integrative analysis of three ‘omics datasets for budding yeast and find clusters of co-expressed genes with shared regulatory proteins. We validate these clusters using data external to the analysis. These clusters can help assign likely function to understudied genes, for example GAS3 clusters with histones active in S-phase, suggesting a role in DNA replication.
Our approach can be used as a wrapper for essentially any existing sampling-based Bayesian clustering implementation, and enables meaningful clustering analyses to be performed using such implementations, even when computational Bayesian inference is not feasible, e.g. due to poor scalability. This enables researchers to straightforwardly extend the applicability of existing software to much larger datasets, including implementations of sophisticated models such as those that jointly model multiple datasets.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
paul.kirk{at}mrc-bsu.cam.ac.uk, cew54{at}cam.ac.uk
Introduction rewritten to more clearly explain motivation and contribution of the method
Abbreviations
- ARI
- Adjusted Rand Index
- ChIP-chip
- Chromatin immunoprecipitation followed by microarray hybridization
- CM
- Consensus Matrix
- MCMC
- Markov chain Monte Carlo
- MDI
- Multiple Dataset Integration
- PCA
- Principal Component Analysis
- PPI
- Protein-Protein Interaction
- PSM
- Posterior Similarity Matrix
- SSE
- Sum of Squared Errors
- TF
- Transcription Factor