Cohesion and Repulsion in Bayesian Distance Clustering

TL;DR

This paper introduces a Bayesian distance clustering method that incorporates both cohesion and repulsion to improve cluster identifiability and scalability in high-dimensional data analysis.

Contribution

It proposes a novel likelihood model with cohesion and repulsion terms, enhancing probabilistic clustering with better interpretability and computational efficiency.

Findings

Method is computationally efficient

Effective in high-dimensional clustering scenarios

Demonstrated success in simulation and digital numismatics

Abstract

Clustering in high-dimensions poses many statistical challenges. While traditional distance-based clustering methods are computationally feasible, they lack probabilistic interpretation and rely on heuristics for estimation of the number of clusters. On the other hand, probabilistic model-based clustering techniques often fail to scale and devising algorithms that are able to effectively explore the posterior space is an open problem. Based on recent developments in Bayesian distance-based clustering, we propose a hybrid solution that entails defining a likelihood on pairwise distances between observations. The novelty of the approach consists in including both cohesion and repulsion terms in the likelihood, which allows for cluster identifiability. This implies that clusters are composed of objects which have small "dissimilarities" among themselves (cohesion) and similar dissimilarities to observations in other clusters (repulsion). We show how this modelling strategy has interesting connection with existing proposals in the literature as well as a decision-theoretic interpretation. The proposed method is computationally efficient and applicable to a wide variety of scenarios. We demonstrate the approach in a simulation study and an application in digital numismatics.