The Bayesian information criterion is generic in the sense that it does not include information about the specific model selection problem at hand. Nevertheless, it has been widely used to estimate the number of data clusters in cluster analysis. We have recently derived a Bayesian cluster enumeration criterion from first principles which maximizes the posterior probability of the candidate models given observations. But, in the finite sample regime, the asymptotic assumptions made by the criterion, to arrive at a computationally simple penalty term, are violated. Hence, we propose a Bayesian cluster enumeration criterion whose penalty term is derived by removing the asymptotic assumptions. The proposed algorithm is a twostep
approach which uses a model-based clustering algorithm such as the EM algorithm before applying the derived criterion.
Simulation results demonstrate the superiority of our criterion over existing Bayesian cluster enumeration criteria.