CliPS -- How to identify cluster distributions in Bayesian mixture models

2026-02-27

AI Summary

Identifying, evaluating, and validating clustering structures in Bayesian mixture models has long been hindered by the complexity of the posterior distribution. This work proposes CliPS, a novel approach that reformulates mixture models as point processes and introduces a low-dimensional parametric functional mapping to transform MCMC samples. By leveraging the separability between the point process representation and the functional mapping, CliPS simultaneously accomplishes cluster identification, assessment of solution quality, and structural validation within the posterior space. The method effectively extracts distinguishable clustering patterns by isolating interpretable features from complex posterior geometries. Extensive experiments on both simulated and real-world datasets demonstrate that CliPS reliably recovers well-separated cluster distributions, confirming its effectiveness and broad applicability across diverse data scenarios.

Technology Category

• Machine Learning: Clustering
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We propose the CliPS procedure when fitting Bayesian mixture models in the context of model-based clustering to identify the cluster distributions while simultaneously assessing the suitability of a cluster solution and validating the cluster structure. The procedure relies on the point process representation of a mixture model and is based on the assumption that a suitable cluster solution requires the clusters to be distinguishable with respect to a low-dimensional functional of the component-specific parameters of the mixture. CliPS maps the component-specific MCMC draws to the point process representation and identifies clusters there, exploiting that, while data distributions usually overlap, the posterior of these functionals are more and more separated for increasing sample size. We outline the procedure and illustrate its use on several model-based clustering examples.

Problem

• Bayesian mixture models
• model-based clustering
• cluster identification
• point process representation
• cluster validation

Innovation

• CliPS
• Bayesian mixture models
• point process representation
• model-based clustering
• low-dimensional functional