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

TL;DR

This paper introduces a flexible framework for clustering that incorporates stochastic pairwise constraints, enabling the modeling of fairness and semi-supervised learning, with provable approximation guarantees and experimental validation.

Contribution

It develops a general approximation framework for clustering with stochastic pairwise constraints, covering applications like fairness and semi-supervised learning, with improved results for Must-link constraints.

Findings

Algorithms with provable guarantees for clustering with constraints

Effective modeling of fairness and semi-supervised learning scenarios

Experimental validation of algorithm effectiveness

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.