Mean-field theory of Bayesian clustering

Alexander Mozeika, Anthony CC Coolen

Published 2017-09-05Version 1

We map model-based Bayesian clustering, which is based on stochastic partitioning of data, into a statistical physics problem for a gas of particles. Using mean-field theory we show that, under natural assumptions, the lowest entropy state of this hypothetical `gas' corresponds to the optimal clustering of data. The byproduct of our analysis is a simple but effective clustering algorithm, which infers both the most plausible number of clusters and the corresponding partitions.