Bayesian Clustering via Fusing of Localized Densities

TL;DR

FOLD is a Bayesian clustering method that fuses localized densities to improve robustness against kernel misspecification, providing better cluster inference and uncertainty quantification.

Contribution

The paper introduces FOLD, a novel Bayesian clustering approach that fuses kernel components, addressing kernel misspecification issues and enhancing cluster detection.

Findings

FOLD outperforms competitors in simulations and real data.

FOLD reduces the number of clusters while maintaining meaningful groupings.

Provides theoretical support for clustering optimality under misspecification.

Abstract

Bayesian clustering typically relies on mixture models, with each component interpreted as a different cluster. After defining a prior for the component parameters and weights, Markov chain Monte Carlo (MCMC) algorithms are commonly used to produce samples from the posterior distribution of the component labels. The data are then clustered by minimizing the expectation of a clustering loss function that favours similarity to the component labels. Unfortunately, although these approaches are routinely implemented, clustering results are highly sensitive to kernel misspecification. For example, if Gaussian kernels are used but the true density of data within a cluster is even slightly non-Gaussian, then clusters will be broken into multiple Gaussian components. To address this problem, we develop Fusing of Localized Densities (FOLD), a novel clustering method that melds components together using the posterior of the kernels. FOLD has a fully Bayesian decision theoretic justification, naturally leads to uncertainty quantification, can be easily implemented as an add-on to MCMC algorithms for mixtures, and favours a small number of distinct clusters. We provide theoretical support for FOLD including clustering optimality under kernel misspecification. In simulated experiments and real data, FOLD outperforms competitors by minimizing the number of clusters while inferring meaningful group structure.