Fair Clustering via Alignment

TL;DR

This paper introduces FCA, a novel fair clustering algorithm that balances fairness and utility by aligning data distributions, providing theoretical guarantees and outperforming existing methods in experiments.

Contribution

Proposes FCA, a new fair clustering algorithm based on data alignment that guarantees near-optimal utility without complex constraints.

Findings

FCA achieves a better fairness-utility trade-off.

FCA attains near-perfect fairness.

FCA demonstrates numerical stability in experiments.

Abstract

Algorithmic fairness in clustering aims to balance the proportions of instances assigned to each cluster with respect to a given sensitive attribute. While recently developed fair clustering algorithms optimize clustering objectives under specific fairness constraints, their inherent complexity or approximation often results in suboptimal clustering utility or numerical instability in practice. To resolve these limitations, we propose a new fair clustering algorithm based on a novel decomposition of the fair $K$-means clustering objective function. The proposed algorithm, called Fair Clustering via Alignment (FCA), operates by alternately (i) finding a joint probability distribution to align the data from different protected groups, and (ii) optimizing cluster centers in the aligned space. A key advantage of FCA is that it theoretically guarantees approximately optimal clustering utility for any given fairness level without complex constraints, thereby enabling high-utility fair clustering in practice. Experiments show that FCA outperforms existing methods by (i) attaining a superior trade-off between fairness level and clustering utility, and (ii) achieving near-perfect fairness without numerical instability.