Bayesian repulsive mixture model for multivariate functional data

TL;DR

This paper presents a Bayesian repulsive mixture model for clustering multivariate functional data, incorporating covariates and a novel MCMC sampling method to improve cluster differentiation and avoid redundancy.

Contribution

It introduces a repulsive prior for multivariate functional data clustering, extending existing priors and including a novel split-merge MCMC algorithm for better posterior sampling.

Findings

Model effectively identifies well-differentiated clusters in simulations.

Repulsive prior reduces redundant clusters and improves interpretability.

Application to CAI data successfully groups individuals by movement pattern similarities.

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.