ICML 2025

Fair Clustering via Alignment
Kunwoong Kim 1 Jihu Lee 1 Sangchul Park 2 Yongdai Kim 1
Abstract
Algorithmic fairness in clustering aims to bal-
ance the proportions of instances assigned to
each cluster with respect to a given sensitive at-
tribute. While recently developed fair clustering
algorithms optimize clustering objectives under
specific fairness constraints, their inherent com-
plexity or approximation often results in subopti-
mal 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 ob-
jective function. The proposed algorithm, called
Fair Clustering via Alignment (FCA), operates
by alternately (i) finding a joint probability distri-
bution 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 with-
out 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.
1. Introduction
As artificial intelligence (AI) technology has advanced and
been successfully applied to diverse domains and tasks, the
requirement for AI systems to make fair decisions (i.e., al-
gorithmic fairness) has emerged as an important societal
issue. This requirement is particularly necessary when ob-
served data possess historical biases with respect to specific
sensitive attributes, leading to unfair outcomes of learned
models based on such biased data (Angwin et al., 2016;
1Department of Statistics, Seoul National University, Re-
public of Korea 2School of Law, Seoul National University,
Republic of Korea.
Correspondence to: Yongdai Kim <yd...