  Bayesian model-based clustering is a widely applied procedure for discovering
groups of related observations in a dataset. These approaches use Bayesian
mixture models, estimated with MCMC, which provide posterior samples of the
model parameters and clustering partition. While inference on model parameters
is well established, inference on the clustering partition is less developed. A
new method is developed for estimating the optimal partition from the pairwise
posterior similarity matrix generated by a Bayesian cluster model. This
approach uses non-negative matrix factorization (NMF) to provide a low-rank
approximation to the similarity matrix. The factorization permits hard or soft
partitions and is shown to perform better than several popular alternatives
under a variety of penalty functions.
