Cluster-level Group Representativity Fairness in $k$-means Clustering

TL;DR

This paper introduces a fair clustering algorithm that improves group representation fairness within clusters, focusing on the worst-off group, with empirical evidence showing significant fairness improvements with minimal impact on cluster quality.

Contribution

The paper proposes a novel iterative optimization method for fair clustering that specifically targets the worst-off group within each cluster, enhancing fairness without greatly sacrificing cluster coherence.

Findings

Significant improvement in cluster-level group fairness.

Minimal reduction in cluster coherence.

Effective across multiple real-world datasets.

Abstract

There has been much interest recently in developing fair clustering algorithms that seek to do justice to the representation of groups defined along sensitive attributes such as race and gender. We observe that clustering algorithms could generate clusters such that different groups are disadvantaged within different clusters. We develop a clustering algorithm, building upon the centroid clustering paradigm pioneered by classical algorithms such as $k$-means, where we focus on mitigating the unfairness experienced by the most-disadvantaged group within each cluster. Our method uses an iterative optimisation paradigm whereby an initial cluster assignment is modified by reassigning objects to clusters such that the worst-off sensitive group within each cluster is benefitted. We demonstrate the effectiveness of our method through extensive empirical evaluations over a novel evaluation metric on real-world datasets. Specifically, we show that our method is effective in enhancing cluster-level group representativity fairness significantly at low impact on cluster coherence.