MCMC Clustering and Its Convergence Issues

• Activity Number: 421
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: SSC
• Author(s): Namdar Homayounfar*+ and Masoud Asgharian and Vahid Partovi Nia
• Companies: and McGill University and École Polytechnique Montréal
• Keywords: Metropolis-Hasting algorithm ; Bayesian clustering ; Convergence ; Gibbs sampling ; Split-Merge algorithm

Abstract

Bayesian clustering using MCMC sampling is a popular approach. When a Markov chain Monte Carlo method is applied, the Markov chain samples are used to approximate the posterior after the chain is converged. When the data grouping is the concern, the convergence must be checked over the allocation space. The convergence of a Markov chain is verified, often using a trace plot, or using other common quantitative criteria mostly designed for a continuous state space. However, data allocation is a very large unordered discrete space and therefore the common convergence criteria is nontrivial to apply. We monitor the convergence of a clustering chain by a convergence criterion devised for the data allocation space.