Fair Clustering Under a Bounded Cost

TL;DR

This paper addresses fair clustering by bounding the clustering cost and maximizing fairness, introducing algorithms with guarantees for different fairness objectives and validating them on real datasets.

Contribution

It proposes a new approach to fair clustering by constraining cost and optimizing fairness, with theoretical bounds and practical algorithms.

Findings

Algorithms with provable guarantees for utilitarian and egalitarian fairness.

Fundamental lower bounds on approximation for certain fairness objectives.

Experimental validation on real-world datasets.

Abstract

Clustering is a fundamental unsupervised learning problem where a dataset is partitioned into clusters that consist of nearby points in a metric space. A recent variant, fair clustering, associates a color with each point representing its group membership and requires that each color has (approximately) equal representation in each cluster to satisfy group fairness. In this model, the cost of the clustering objective increases due to enforcing fairness in the algorithm. The relative increase in the cost, the ''price of fairness,'' can indeed be unbounded. Therefore, in this paper we propose to treat an upper bound on the clustering objective as a constraint on the clustering problem, and to maximize equality of representation subject to it. We consider two fairness objectives: the group utilitarian objective and the group egalitarian objective, as well as the group leximin objective which generalizes the group egalitarian objective. We derive fundamental lower bounds on the approximation of the utilitarian and egalitarian objectives and introduce algorithms with provable guarantees for them. For the leximin objective we introduce an effective heuristic algorithm. We further derive impossibility results for other natural fairness objectives. We conclude with experimental results on real-world datasets that demonstrate the validity of our algorithms.