Fairness, Semi-Supervised Learning, and More: A General Framework for Clustering with Stochastic Pairwise Constraints

• URL: http://arxiv.org/abs/2103.02013v1
• Date: Tue, 2 Mar 2021 20:27:58 GMT
• Title: Fairness, Semi-Supervised Learning, and More: A General Framework for Clustering with Stochastic Pairwise Constraints
• Authors: Brian Brubach, Darshan Chakrabarti, John P. Dickerson, Aravind Srinivasan, Leonidas Tsepenekas
• Abstract summary: We introduce a novel family of emphstochastic pairwise constraints, which we incorporate into several essential clustering objectives. We show that these constraints can succinctly model an intriguing collection of applications, including emphIndividual Fairness in clustering and emphMust-link constraints in semi-supervised learning.
• Score: 32.19047459493177
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 \emph{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 \emph{Individual Fairness} in clustering and \emph{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.

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