2021/03/02 by Brian Brubach, Darshan Chakrabarti, Brubach, Brian +7 · 2 citations
Computer Science · #Advanced Clustering Algorithms Research #Data Management and Algorithms #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Machine Learning (cs.LG) #cs.DS #cs.LG
paper · pdf · doi:10.48550/arxiv.2103.02013
This paper appeared in AAAI 2021
arxiv created 2021/03/02 · openalex publication_date 2021/03/02 · arxiv updated 2021/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Metric clustering is fundamental in areas ranging from Combinatorial Optimization and Data Mining, to Machine Learning and Operations Research. However, in a variety of situations we may have additional requirements or knowledge, distinct from the underlying metric, regarding which pairs of points should be clustered together. To capture and analyze such scenarios, we introduce a novel family of stochastic pairwise constraints, which we incorporate into several essential clustering objectives (radius/median/means). Moreover, we demonstrate that these constraints can succinctly model an intriguing collection of applications, including among others Individual Fairness in clustering and Must-link constraints in semi-supervised learning. Our main result consists of a general framework that yields approximation algorithms with provable guarantees for important clustering objectives, while at the same time producing solutions that respect the stochastic pairwise constraints. Furthermore, for certain objectives we devise improved results in the case of Must-link constraints, which are also the best possible from a theoretical perspective. Finally, we present experimental evidence that validates the effectiveness of our algorithms.