Graphical model-based clustering of categorical data

TL;DR

This paper introduces a Bayesian clustering method for multivariate categorical data that uses graphical models to explicitly account for variable dependencies within clusters, improving over traditional independence assumptions.

Contribution

It proposes a Dirichlet Process mixture model of categorical graphical models, enabling clustering based on dependence structures and providing full Bayesian inference with MCMC algorithms.

Findings

Graphical model-based clustering outperforms independence-based methods.

The approach effectively captures dependence structures in real datasets.

Simulation studies validate the method's accuracy and robustness.

Abstract

Clustering multivariate data is a pervasive task in many applied problems, particularly in social studies and life science. Model-based approaches to clustering rely on mixture models, where each mixture component corresponds to the kernel of a distribution characterizing a latent sub-group. Current methods developed within this framework employ multivariate distributions built under the assumption of independence among variables given the cluster allocation. Accordingly, possible dependence structures characterizing differences across groups are not directly accounted for during the clustering process. In this paper we consider multivariate categorical data, and introduce a model-based clustering method which employs graphical models as a tool to encode dependencies between variables. Specifically, we consider a Dirichlet Process mixture of categorical graphical models, which clusters individuals into groups that are homogeneous in terms of dependence (graphical) structure and allied parameters. We provide full Bayesian inference for the model and develop a Markov chain Monte Carlo scheme for posterior analysis. Our method is evaluated through simulations and applied to real case studies, including the analysis of genomic data and voting records. Results reveal the merits of a graphical model-based clustering, in comparison with approaches that do not explicitly account for dependencies in the multivariate distribution of variables.