Assessing a mixture model for clustering with the integrated completed likelihood

TLDR

The study proposes a method to assess mixture models in clustering using integrated completed likelihood. The method assigns data to clusters via maximum a posteriori estimation and approximates the integrated completed likelihood with the Bayesian information criterion. Experiments on simulated and real data demonstrate that the ICL criterion accurately selects mixture models and cluster numbers, outperforming BIC in robustness and yielding sensible partitions.

Abstract

We propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood. For this purpose, the observed data are assigned to unknown clusters using a maximum a posteriori operator. Then, the integrated completed likelihood (ICL) is approximated using the Bayesian information criterion (BIC). Numerical experiments on simulated and real data of the resulting ICL criterion show that it performs well both for choosing a mixture model and a relevant number of clusters. In particular, ICL appears to be more robust than BIC to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data.