Hierarchical clustering with discrete latent variable models and the integrated classification likelihood

In this paper, we introduce a two step methodology to extract a hierarchical clustering. This methodology considers the integrated classification likelihood criterion as an objective function, and applies to any discrete latent variable models (DLVM) where this quantity is tractable. The first step of the methodology involves maximizing the criterion with respect to the discrete latent variables state with uninformative priors. To that end we propose a new hybrid algorithm based on greedy local searches as well as a genetic algorithm which allows the joint inference of the number $K$ of clusters and of the clusters themselves. The second step of the methodology is based on a bottom-up greedy procedure to extract a hierarchy of clusters from this natural partition. In a Bayesian context, this is achieved by considering the Dirichlet cluster proportion prior parameter $\alpha$ as a regularisation term controlling the granularity of the clustering. This second step allows the exploration of the clustering at coarser scales and the ordering of the clusters an important output for the visual representations of the clustering results. The clustering results obtained with the proposed approach, on simulated as well as real settings, are compared with existing strategies and are shown to be particularly relevant. This work is implemented in the R package greed.