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

Finding a set of nested partitions dataset is useful to uncover relevant structure at different scales, and often dealt with data-dependent methodology. In this paper, we introduce general two-step methodology for model-based hierarchical clustering. Considering the integrated classification likelihood criterion as an objective function, work applies every discrete latent variable models (DLVMs) where quantity tractable. The first step involves maximizing respect partition. Addressing known problem sub-optimal local maxima found by greedy hill climbing heuristics, new hybrid algorithm based on genetic efficiently exploring space solutions. resulting carefully combines merges solutions, allows joint inference number $K$ clusters well themselves. Starting from natural partition, second bottom-up procedure extract hierarchy clusters. Bayesian context, achieved considering Dirichlet cluster proportion prior parameter $\alpha$ regularization term controlling granularity A approximation derived log-linear function $\alpha$, enabling simple functional form merge decision criterion. This exploration clustering coarser scales. proposed approach compared existing strategies simulated real settings, its results are shown be particularly relevant. reference implementation available in R package greed accompanying paper.