Guarantees for Spectral Clustering with Fairness Constraints

TL;DR

This paper introduces fairness constraints into spectral clustering, providing algorithms that produce fairer clusters and theoretical guarantees for recovering fair clusterings in stochastic block models.

Contribution

It develops new variants of spectral clustering with fairness constraints and offers theoretical analysis showing they can recover fair clusterings with high probability.

Findings

Algorithms produce fairer clusterings on synthetic and real data.

Theoretical guarantees for recovering fair clusters in stochastic block models.

Empirical results demonstrate improved fairness without sacrificing clustering quality.

Abstract

Given the widespread popularity of spectral clustering (SC) for partitioning graph data, we study a version of constrained SC in which we try to incorporate the fairness notion proposed by Chierichetti et al. (2017). According to this notion, a clustering is fair if every demographic group is approximately proportionally represented in each cluster. To this end, we develop variants of both normalized and unnormalized constrained SC and show that they help find fairer clusterings on both synthetic and real data. We also provide a rigorous theoretical analysis of our algorithms on a natural variant of the stochastic block model, where $h$ groups have strong inter-group connectivity, but also exhibit a "natural" clustering structure which is fair. We prove that our algorithms can recover this fair clustering with high probability.