Generalizing Fair Clustering to Multiple Groups: Algorithms and Applications
Diptarka Chakraborty, Kushagra Chatterjee, Debarati Das, Tien-Long Nguyen
TL;DR
The work generalizes closest fair clustering to multiple protected groups and proves NP-hardness for three or more colors, contrasting with the two-color case which admits an exact algorithm. It introduces near-linear time approximation frameworks (notably fairpower-of-two and create-pdc/make-pdc-fair) to handle equi-proportion and arbitrary-proportion group settings, achieving bounds up to $O(|\chi|^{3.81})$-close in general and $O(|\chi|^{1.6})$-type improvements for special cases. The results propagate to fair correlation clustering and, for the first time, to fair consensus clustering with multiple groups, yielding analogous factor guarantees and removing dependence on color-ratio $q$ in some settings. Collectively, the paper advances fair clustering by enabling multi-attribute fairness with provable guarantees and efficient algorithms applicable to practical datasets.
Abstract
Clustering is a fundamental task in machine learning and data analysis, but it frequently fails to provide fair representation for various marginalized communities defined by multiple protected attributes -- a shortcoming often caused by biases in the training data. As a result, there is a growing need to enhance the fairness of clustering outcomes, ideally by making minimal modifications, possibly as a post-processing step after conventional clustering. Recently, Chakraborty et al. [COLT'25] initiated the study of \emph{closest fair clustering}, though in a restricted scenario where data points belong to only two groups. In practice, however, data points are typically characterized by many groups, reflecting diverse protected attributes such as age, ethnicity, gender, etc. In this work, we generalize the study of the \emph{closest fair clustering} problem to settings with an arbitrary number (more than two) of groups. We begin by showing that the problem is NP-hard even when all groups are of equal size -- a stark contrast with the two-group case, for which an exact algorithm exists. Next, we propose near-linear time approximation algorithms that efficiently handle arbitrary-sized multiple groups, thereby answering an open question posed by Chakraborty et al. [COLT'25]. Leveraging our closest fair clustering algorithms, we further achieve improved approximation guarantees for the \emph{fair correlation clustering} problem, advancing the state-of-the-art results established by Ahmadian et al. [AISTATS'20] and Ahmadi et al. [2020]. Additionally, we are the first to provide approximation algorithms for the \emph{fair consensus clustering} problem involving multiple (more than two) groups, thus addressing another open direction highlighted by Chakraborty et al. [COLT'25].