Cohesion and Repulsion in Bayesian Distance Clustering

• 成果类型: Article
• 署名作者: Natarajan, Abhinav; De Iorio, Maria; Heinecke, Andreas; Mayer, Emanuel; Glenn, Simon
• 署名单位: University of Oxford; National University of Singapore; University of London; University College London; Agency for Science Technology & Research (A*STAR); Yale NUS College; University of Oxford; University of Oxford
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2191821
• 发表日期: 2024
• 页码: 1374-1384
• 关键词: dimensional linear-regression; confidence-intervals; variable selection; ridge-regression; Minimax Rates; prediction; Lasso; regions

摘要

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 modeling strategy has interesting connection with existing proposals in the literature. The proposed method is computationally efficient and applicable to a wide variety of scenarios. We demonstrate the approach in simulation and an application in digital numismatics. with code is available online.