Fair Clustering via Alignment

Kunwoong Kim, Sangchul Park, Yongdai Kim

Keywords: Clustering, Fairness, Trustworthy AI

TL;DR: This paper proposes a new algorithm for fair clustering based on a novel decomposition of the fair clustering objective, achieving the optimal trade-off between fairness level and clustering utility for any given fairness level.

Abstract:

Algorithmic fairness in clustering aims to balance the proportions of instances assigned to each cluster with respect to a given sensitive attribute.
Recently, numerous algorithms have been developed for Fair Clustering (FC), most of which optimize a clustering objective under specifically designed fairness constraints.
However, the inherent complexity or approximation of constrained optimization problems makes it challenging to achieve the optimal trade-off between fairness level and clustering utility in practice.
For example, the obtained clustering utility by an existing FC algorithm might be suboptimal, or achieving a certain fairness level could be numerically unstable.
To resolve these limitations, we propose a new FC 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 (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 guarantees (local) optimal clustering utility for any given fairness level while avoiding the need to solve complex constrained optimization problems, thereby obtaining (local) optimal fair clustering in practice.
Experiments show that FCA offers several empirical benefits over existing methods such as (i) attaining the optimal trade-off between fairness level and clustering utility, and (ii) achieving near-perfect fairness level without numerical instability.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

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Submission Number: 9506