  Various methods have been developed to combine inference across multiple sets
of results for unsupervised clustering, within the ensemble clustering
literature. The approach of reporting results from one `best' model out of
several candidate clustering models generally ignores the uncertainty that
arises from model selection, and results in inferences that are sensitive to
the particular model and parameters chosen. Bayesian model averaging (BMA) is a
popular approach for combining results across multiple models that offers some
attractive benefits in this setting, including probabilistic interpretation of
the combined cluster structure and quantification of model-based uncertainty.
  In this work we introduce clusterBMA, a method that enables weighted model
averaging across results from multiple unsupervised clustering algorithms. We
use clustering internal validation criteria to develop an approximation of the
posterior model probability, used for weighting the results from each model.
From a consensus matrix representing a weighted average of the clustering
solutions across models, we apply symmetric simplex matrix factorisation to
calculate final probabilistic cluster allocations. In addition to outperforming
other ensemble clustering methods on simulated data, clusterBMA offers unique
features including probabilistic allocation to averaged clusters, combining
allocation probabilities from 'hard' and 'soft' clustering algorithms, and
measuring model-based uncertainty in averaged cluster allocation. This method
is implemented in an accompanying R package of the same name.
