# Fair Clustering via Alignment

arXiv: https://arxiv.org/abs/2505.09131 · HTML: https://mlsanity.com/paper/2505.09131/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 63 references that are in the map.
- First posted on arXiv 14 May 2025.

## Builds on (most cited first, 28 of 28)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Fair Clustering Through Fairlets](https://mlsanity.com/paper/1802.05733/) (2018)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Fair Algorithms for Clustering](https://mlsanity.com/paper/1901.02393/) (2019)
- [Scalable Fair Clustering](https://mlsanity.com/paper/1902.03519/) (2019)
- [Guarantees for Spectral Clustering with Fairness Constraints](https://mlsanity.com/paper/1901.08668/) (2019)
- [ClusterLLM: Large Language Models as a Guide for Text Clustering](https://mlsanity.com/paper/2305.14871/) (2023)
- [Learning Meta Face Recognition in Unseen Domains](https://mlsanity.com/paper/2003.07733/) (2020)
- [Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections](https://mlsanity.com/paper/2107.01718/) (2021)
- [Scalable Unbalanced Optimal Transport using Generative Adversarial Networks](https://mlsanity.com/paper/1810.11447/) (2018)
- [Statistical Optimal Transport via Factored Couplings](https://mlsanity.com/paper/1806.07348/) (2018)
- [Maximum Flow and Minimum-Cost Flow in Almost-Linear Time](https://mlsanity.com/paper/2203.00671/) (2022)
- [Fair Clustering Under a Bounded Cost](https://mlsanity.com/paper/2106.07239/) (2021)
- [Deep Fair Clustering via Maximizing and Minimizing Mutual Information: Theory, Algorithm and Metric](https://mlsanity.com/paper/2209.12396/) (2022)
- [KFC: A Scalable Approximation Algorithm for k-center Fair Clustering](https://mlsanity.com/paper/2010.13949/) (2020)
- [From Image to Text Classification: A Novel Approach based on Clustering Word Embeddings](https://mlsanity.com/paper/1707.08098/) (2017)
- [Fairness Through Matching](https://mlsanity.com/paper/2501.02793/) (2025)
- [Efficient Algorithms For Fair Clustering with a New Fairness Notion](https://mlsanity.com/paper/2109.00708/) (2021)

## Built on by (most cited first, 1 of 1)

- [COVAriance-Induced Fairness Gap Penalty for Subgroup-Fair Clustering](https://mlsanity.com/paper/2607.18119/) (2026)

## Abstract (arXiv)

Algorithmic fairness in clustering aims to balance the proportions of instances assigned to each cluster with respect to a given sensitive attribute. While recently developed fair clustering algorithms optimize clustering objectives under specific fairness constraints, their inherent complexity or approximation often results in suboptimal 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 objective function. The proposed algorithm, called Fair Clustering via Alignment (FCA), operates by alternately (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 theoretically guarantees approximately optimal clustering utility for any given fairness level without 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.