# Variational Fair Clustering

arXiv: https://arxiv.org/abs/1906.08207 · HTML: https://mlsanity.com/paper/1906.08207/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2019.

## Built on by (most cited first, 3 of 3)

- [A Stochastic Alternating Balance k-Means Algorithm for Fair Clustering](https://mlsanity.com/paper/2105.14172/) (2021)
- [Fair Clustering Using Antidote Data](https://mlsanity.com/paper/2106.00600/) (2021)
- [Fairness Degrading Adversarial Attacks Against Clustering Algorithms](https://mlsanity.com/paper/2110.12020/) (2021)

## Abstract (arXiv)

We propose a general variational framework of fair clustering, which integrates an original Kullback-Leibler (KL) fairness term with a large class of clustering objectives, including prototype or graph based. Fundamentally different from the existing combinatorial and spectral solutions, our variational multi-term approach enables to control the trade-off levels between the fairness and clustering objectives. We derive a general tight upper bound based on a concave-convex decomposition of our fairness term, its Lipschitz-gradient property and the Pinsker's inequality. Our tight upper bound can be jointly optimized with various clustering objectives, while yielding a scalable solution, with convergence guarantee. Interestingly, at each iteration, it performs an independent update for each assignment variable. Therefore, it can be easily distributed for large-scale datasets. This scalability is important as it enables to explore different trade-off levels between the fairness and clustering objectives. Unlike spectral relaxation, our formulation does not require computing its eigenvalue decomposition. We report comprehensive evaluations and comparisons with state-of-the-art methods over various fair-clustering benchmarks, which show that our variational formulation can yield highly competitive solutions in terms of fairness and clustering objectives.