Bayesian repulsive mixture model for multivariate functional data

2026-03-07

AI Summary

This study addresses the challenges of redundant clusters and the difficulty of incorporating individual covariates in clustering multivariate functional data. To this end, we propose a Bayesian mixture model equipped with a repulsive prior, extended to the multivariate functional setting. The approach represents functional curves using B-spline basis functions and constructs a shape-aware distance metric that integrates covariate information. An efficient split-merge Markov chain Monte Carlo (MCMC) algorithm is further developed to enhance posterior sampling efficiency. Simulation studies demonstrate that the proposed model effectively mitigates redundant clustering, improves cluster identifiability, and successfully identifies clinically meaningful subgroups with similar movement dysfunction patterns in real-world data on chronic ankle instability.

Technology Category

• Machine Learning: Clustering
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Mining of Visual, Multimedia & Multimodal Data

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

We introduce a repulsive mixture model to cluster observation units represented by multivariate functional data, based on similarity of curve shapes and individual-specific covariates. We propose a repulsive prior distribution for the component-specific location parameters that depends on a B-spline curve-tailored distance, extending existent repulsive priors to the context of multivariate functional data. The proposed model favors the identification of well-differentiated clusters, avoiding the presence of redundant ones. To sample from the posterior distribution, we propose an MCMC algorithm that includes a novel split-merge step that significantly improves the chain mixing. Different features of the proposed model, including the effects of repulsion and covariates in the clustering, are evaluated through simulation. The proposed model is fitted to analyze Chronic Ankle Instability (CAI) data, focusing on identifing individuals with similar types of physical dysfunctions based on the similarity of movement patterns.

Problem

• multivariate functional data
• clustering
• Chronic Ankle Instability
• curve shapes
• individual-specific covariates

Innovation

• repulsive mixture model
• multivariate functional data
• B-spline distance
• split-merge MCMC
• Bayesian clustering