Bayesian Clustering Factor Models

2025-05-08

AI Summary

High-dimensional heterogeneous healthcare data—such as those from opioid use disorder (OUD) recovery studies—pose challenges in jointly performing dimensionality reduction and clustering. Method: We propose a Bayesian joint factor-clustering model that employs a Gaussian mixture prior over latent variables and establishes a hierarchical factor analysis framework to simultaneously achieve dimensionality reduction and subject-level clustering. Contribution/Results: This work is the first to unify factor modeling with Bayesian clustering; it introduces a novel information criterion that jointly selects the optimal number of clusters and latent factors, and quantifies inference uncertainty explicitly via Gibbs sampling. Simulation studies demonstrate substantially improved structural recovery accuracy over existing methods. Applied to real OUD recovery data, the model successfully identifies clinically meaningful recovery subgroups, yielding interpretable, actionable clusters for personalized intervention strategies.

Technology Category

• Machine Learning: Clustering
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

We present a novel framework for concomitant dimension reduction and clustering. This framework is based on a novel class of Bayesian clustering factor models. These models assume a factor model structure where the vectors of common factors follow a mixture of Gaussian distributions. We develop a Gibbs sampler to explore the posterior distribution and propose an information criterion to select the number of clusters and the number of factors. Simulation studies show that our inferential approach appropriately quantifies uncertainty. In addition, when compared to a previously published competitor method, our information criterion has favorable performance in terms of correct selection of number of clusters and number of factors. Finally, we illustrate the capabilities of our framework with an application to data on recovery from opioid use disorder where clustering of individuals may facilitate personalized health care.

Problem

• Develop Bayesian clustering factor models for dimension reduction and clustering
• Propose Gibbs sampler and information criterion for cluster and factor selection
• Apply framework to opioid recovery data for personalized healthcare clustering

Innovation

• Bayesian clustering factor models framework
• Gibbs sampler for posterior distribution
• Information criterion for cluster selection