Choosing the number of clusters in a finite mixture model using an exact Integrated Completed Likelihood criterion

TL;DR

This paper derives an exact expression for the integrated completed likelihood (ICL) in mixture models using conjugate priors, enabling precise selection of the number of clusters and observation allocations without approximation.

Contribution

It introduces an exact ICL formula for mixture models and a unified algorithm to determine the optimal number of clusters and data allocation.

Findings

Exact ICL avoids approximation errors.

Algorithm performs well on simulated data.

Effective in real-world clustering scenarios.

Abstract

The integrated completed likelihood (ICL) criterion has proven to be a very popular approach in model-based clustering through automatically choosing the number of clusters in a mixture model. This approach effectively maximises the complete data likelihood, thereby including the allocation of observations to clusters in the model selection criterion. However for practical implementation one needs to introduce an approximation in order to estimate the ICL. Our contribution here is to illustrate that through the use of conjugate priors one can derive an exact expression for ICL and so avoiding any approximation. Moreover, we illustrate how one can find both the number of clusters and the best allocation of observations in one algorithmic framework. The performance of our algorithm is presented on several simulated and real examples.