Title: UniFair: A Unified Fair Clustering Approach Grounded in Separation and Compactness

Abstract:

As clustering techniques become pivotal in driving high-stakes decision-making, standard algorithms like $k$-means often generate groupings that unfairly discriminate against specific demographic segments. While current fair clustering methodologies typically focus on a singular definition of equity, they frequently neglect the interplay between clustering costs and the geometry of the resulting decision boundaries. To address these limitations, we introduce \textsc{UniFair}, a comprehensive framework that simultaneously optimizes \emph{separation fairness} and \emph{social fairness}. Separation fairness is designed to position protected groups at a greater distance from the induced decision boundaries, whereas social fairness aims to minimize disparities in within-cluster distortion by imposing penalties on group-specific clustering costs. We have developed gradient-based optimization strategies for both separation-fair and unified $k$-means objectives, further extending these methods to deep clustering by applying identical constraints within an autoencoder’s latent space. Our empirical evaluations on both image and tabular datasets demonstrate that \textsc{UniFair} effectively mitigates disparities related to both boundaries and costs, achieving this balance with only a slight increase in overall clustering loss.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC