Assessing a mixture model for clustering with the integrated completed likelihood

We propose assessing a mixture model in a cluster analysis setting with the integrated completed likelihood. With 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 an a` la 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 clusters leading to a sensible partitioning of the data.