Exact ratio preservation via outliers for fair $k$-center clustering

2026-07-06

AI Summary

This work addresses the challenge of achieving strictly fair clustering when input data do not conform to the desired group proportions. Building upon the fair clustering framework of Chierichetti et al., the authors propose a novel fair k-center clustering method that integrates an outlier-aware mechanism within a combinatorial optimization formulation. Their approach is the first to exactly satisfy multi-group fairness constraints under arbitrary integer group ratios (e.g., t₁:t₂:…:tₘ), overcoming the limitations of existing methods that either assume balanced data or settle for approximate fairness. The paper presents a constant-factor approximation algorithm and demonstrates through empirical evaluation its effectiveness and scalability in practical scenarios.

Abstract

We study the $k$-center clustering problem under demographic fairness constraints, where the point set is partitioned into groups, and the aim is to compute clusters that exhibit a given group proportion. Previous work in this direction assumes that the entire point set already respects the desired proportions or uses relaxed notions of fairness. In this work, we propose a model that facilitates the creation of clusters that exactly match given target ratios, even when the input point set does not. We combine the well-known fair clustering model initiated by Chierichetti, Kumar, Lattanzi, and Vassilvitskii (NeurIPS 2017) with the notion of outliers to obtain a practical combinatorial framework that provides constant-factor approximate solutions for all proportion settings from $1:1$ for two groups to $t_1:t_2:\ldots:t_m$ for $m\geq 2$ groups, where $t_1,\ldots,t_m$ are integers. We implement and evaluate our algorithms, compare different variants, and provide evidence of the practicability of this approach.

Problem

• fair clustering
• k-center
• demographic fairness
• outliers
• ratio preservation

Innovation

• fair clustering
• k-center
• outliers
• exact ratio preservation
• demographic fairness