Posterior Regularization on Bayesian Hierarchical Mixture Clustering

TL;DR

This paper enhances Bayesian hierarchical mixture clustering by applying Posterior Regularization to improve cluster separation and reduce high variance in hierarchical trees.

Contribution

It introduces a novel application of Posterior Regularization to BHMC, enforcing max-margin constraints for better hierarchical clustering.

Findings

Improved cluster separation in hierarchical trees

Reduction in high nodal variance

Enhanced model robustness

Abstract

Bayesian hierarchical mixture clustering (BHMC) improves traditionalBayesian hierarchical clustering by replacing conventional Gaussian-to-Gaussian kernels with a Hierarchical Dirichlet Process Mixture Model(HDPMM) for parent-to-child diffusion in the generative process. However,BHMC may produce trees with high nodal variance, indicating weak separation between nodes at higher levels. To address this issue, we employ Posterior Regularization, which imposes max-margin constraints on nodes at every level to enhance cluster separation. We illustrate how to apply PR toBHMC and demonstrate its effectiveness in improving the BHMC model.