🤖 AI Summary
This work proposes a nonparametric Bayesian clustering approach for multivariate categorical data that explicitly incorporates graphical models to account for heterogeneous dependence structures across clusters. Unlike conventional methods that assume conditional independence of variables within each cluster, the proposed framework employs a Dirichlet process mixture of categorical graphical models to partition individuals into groups that are homogeneous not only in marginal distributions but also in their underlying dependency structures and associated parameters. Full Bayesian inference is performed via Markov chain Monte Carlo (MCMC) to enable posterior analysis. To the best of our knowledge, this is the first method to explicitly integrate graphical models into the clustering of categorical data, thereby effectively capturing inter-group differences in dependence patterns. Experiments on simulated data as well as real-world genomic and voting records demonstrate that the approach significantly outperforms existing methods that ignore such structural dependencies.
📝 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.