# clusterBMA: Bayesian model averaging for clustering

**Authors:** Owen Forbes, Edgar Santos-Fernandez, Paul Pao-Yen Wu, Hong-Bo Xie, Paul E. Schwenn, Jim Lagopoulos, Lia Mills, Dashiell D. Sacks, Daniel F. Hermens, Kerrie Mengersen  
**arXiv:** [2209.04117](https://arxiv.org/abs/2209.04117)  
**Date:** 2022-09-09  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2209.04117v2/

## Key points

- The paper introduces clusterBMA, a method for weighted model averaging across multiple unsupervised clustering algorithms.
- Bayesian model averaging (BMA) is proposed to combine results from multiple models, providing a probabilistic interpretation of the combined cluster structure and quantifying model-based uncertainty.
- Internal validation criteria are used to approximate posterior model probabilities for weighting results from each model.
- A consensus matrix is constructed to represent a weighted average of clustering solutions across models, with symmetric simplex matrix factorization applied to calculate final probabilistic cluster allocations.
- The method outperforms other ensemble clustering methods on simulated data and offers unique features such as probabilistic allocation to averaged clusters, combining 'hard' and 'soft' clustering algorithms, and measuring model-based uncertainty in averaged cluster allocation.
- The innovative method is implemented in an accompanying R package named [package name].
- Overall, the paper provides a comprehensive framework for combining inference across multiple sets of results for unsupervised clustering through Bayesian model averaging, addressing uncertainties associated with model selection in ensemble clustering literature.

## Summary

The paper "clusterBMA: Bayesian model averaging for clustering" by Owen Forbes, Edgar Santos-Fernandez, Paul Pao-Yen Wu, Hong-Bo Xie, Paul E. Schwenn, Jim Lagopoulos, Lia Mills, Dashiell D. Sacks, Daniel F. Hermens, and Kerrie Mengersen introduces a method for weighted model averaging across results from multiple unsupervised clustering algorithms. The traditional approach of selecting the 'best' model out of several candidate clustering models often overlooks the uncertainty arising from model selection. This can lead to sensitive inferences that are dependent on specific models and parameters chosen. <br/><br/>
 (BMA) is proposed as a solution to effectively combine results across multiple models by providing a probabilistic interpretation of the combined cluster structure and quantifying model-based uncertainty. The  method utilized in this paper utilizes internal validation criteria to approximate posterior model probabilities for weighting results from each model.<br/><br/>
By constructing a consensus matrix that represents a weighted average of clustering solutions across models,, symmetric simplex matrix factorization is applied to calculate final probabilistic cluster allocations. Notably, outperforms other ensemble clustering methods on simulated data and offers unique features such as probabilistic allocation to averaged clusters, combining allocation probabilities from both 'hard' and 'soft' clustering algorithms, and measuring model-based uncertainty in averaged cluster allocation.<br/><br/>
This innovative method presented in the paper is implemented in an accompanying R package named . Overall, the paper provides a comprehensive framework for combining inference across multiple sets of results for unsupervised clustering through Bayesian model averaging, offering significant advancements in addressing uncertainties associated with model selection in ensemble clustering literature.