Welfare-Centric Clustering

TL;DR

This paper introduces a welfare-centric clustering framework that models group utilities based on distances and representation, proposing new algorithms with theoretical guarantees and demonstrating superior performance over existing fair clustering methods.

Contribution

It formalizes welfare-centric clustering objectives and develops novel algorithms with proven guarantees, advancing fair clustering research.

Findings

Algorithms outperform existing fair clustering baselines

Theoretical guarantees established for proposed algorithms

Empirical results show significant improvements on real-world datasets

Abstract

Fair clustering has traditionally focused on ensuring equitable group representation or equalizing group-specific clustering costs. However, Dickerson et al. (2025) recently showed that these fairness notions may yield undesirable or unintuitive clustering outcomes and advocated for a welfare-centric clustering approach that models the utilities of the groups. In this work, we model group utilities based on both distances and proportional representation and formalize two optimization objectives based on welfare-centric clustering: the Rawlsian (Egalitarian) objective and the Utilitarian objective. We introduce novel algorithms for both objectives and prove theoretical guarantees for them. Empirical evaluations on multiple real-world datasets demonstrate that our methods significantly outperform existing fair clustering baselines.