The Conditional-Potts Clustering Model

A Bayesian kernel-based clustering method is presented. The associated model arises as an embedding of the Potts density for label membership probabilities into an extended Bayesian model for joint data and label membership probabilities. The method may be seen as a principled extension of the so-called super-paramagnetic clustering. The model depends on three parameters: the temperature, the kernel bandwidth and the joint pair-membership probability threshold. We elucidate an informative prior based on random graph theory and kernel density estimation. The clustering is estimated automatically by setting the parameters at the modes of their posteriors. Two stochastic Wang-Landau-like algorithms are presented to estimate the posteriors. We also develop an efficient clustering procedure based only on the modes of our informative prior.