Minimum Message Length Clustering Using Gibbs Sampling

Abstract

The K-Means and EM algorithms are popular in clustering and mixture modeling due to their simplicity and ease of implementation. However, they have several significant limitations. Both converge to a local optimum of their respective objective functions (ignoring the uncertainty in the model space), require the apriori specification of the number of classes/clusters, and are inconsistent. In this work we overcome these limitations by using the Minimum Message Length (MML) principle and a variation to the K-Means/EM observation assignment and parameter calculation scheme. We maintain the simplicity of these approaches while constructing a Bayesian mixture modeling tool that samples/searches the model space using a Markov Chain Monte Carlo (MCMC) sampler known as a Gibbs sampler. Gibbs sampling allows us to visit each model according to its posterior probability. Therefore, if the model space is multi-modal we will visit all modes and not get stuck in local optima. We call our approach multiple chains at equilibrium (MCE) MML sampling.