# Deep Fair Clustering via Maximizing and Minimizing Mutual Information: Theory, Algorithm and Metric

arXiv: https://arxiv.org/abs/2209.12396 · HTML: https://mlsanity.com/paper/2209.12396/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 52 references that are in the map.
- First posted on arXiv 26 Sep 2022.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Contrastive Clustering](https://mlsanity.com/paper/2009.09687/) (2020)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Fair Clustering Through Fairlets](https://mlsanity.com/paper/1802.05733/) (2018)
- [Learning Discrete Representations via Information Maximizing Self-Augmented Training](https://mlsanity.com/paper/1702.08720/) (2017)
- [Deep Clustering via Joint Convolutional Autoencoder Embedding and Relative Entropy Minimization](https://mlsanity.com/paper/1704.06327/) (2017)
- [50 Years of Test (Un)fairness: Lessons for Machine Learning](https://mlsanity.com/paper/1811.10104/) (2018)
- [Fair Algorithms for Clustering](https://mlsanity.com/paper/1901.02393/) (2019)
- [Scalable Fair Clustering](https://mlsanity.com/paper/1902.03519/) (2019)
- [ClusterGAN : Latent Space Clustering in Generative Adversarial Networks](https://mlsanity.com/paper/1809.03627/) (2018)
- [Guarantees for Spectral Clustering with Fairness Constraints](https://mlsanity.com/paper/1901.08668/) (2019)
- [Deep Spectral Clustering using Dual Autoencoder Network](https://mlsanity.com/paper/1904.13113/) (2019)
- [Proportionally Fair Clustering](https://mlsanity.com/paper/1905.03674/) (2019)
- [Fair k-Center Clustering for Data Summarization](https://mlsanity.com/paper/1901.08628/) (2019)
- [Individual Fairness for k-Clustering](https://mlsanity.com/paper/2002.06742/) (2020)
- [Clustering without Over-Representation](https://mlsanity.com/paper/1905.12753/) (2019)
- [A Pairwise Fair and Community-preserving Approach to k-Center Clustering](https://mlsanity.com/paper/2007.07384/) (2020)
- [Deep Fair Discriminative Clustering](https://mlsanity.com/paper/2105.14146/) (2021)
- [Towards Fair Deep Clustering With Multi-State Protected Variables](https://mlsanity.com/paper/1901.10053/) (2019)
- [Unified Spectral Clustering with Optimal Graph](https://mlsanity.com/paper/1711.04258/) (2017)

## Built on by (most cited first, 17 of 17)

- [Image Clustering Conditioned on Text Criteria](https://mlsanity.com/paper/2310.18297/) (2023)
- [Fairness in Visual Clustering: A Novel Transformer Clustering Approach](https://mlsanity.com/paper/2304.07408/) (2023)
- [A Survey on Deep Clustering: From the Prior Perspective](https://mlsanity.com/paper/2406.19602/) (2024)
- [Exploring a Principled Framework for Deep Subspace Clustering](https://mlsanity.com/paper/2503.17288/) (2025)
- ["X of Information'' Continuum: A Survey on AI-Driven Multi-dimensional Metrics for Next-Generation Networked Systems](https://mlsanity.com/paper/2507.19657/) (2025)
- [A Unified Framework for Fair Spectral Clustering With Effective Graph Learning](https://mlsanity.com/paper/2311.13766/) (2023)
- [Robust Fair Clustering with Group Membership Uncertainty Sets](https://mlsanity.com/paper/2406.00599/) (2024)
- [Fair Clustering via Alignment](https://mlsanity.com/paper/2505.09131/) (2025)
- [From Discrete to Continuous: Deep Fair Clustering With Transferable Representations](https://mlsanity.com/paper/2403.16201/) (2024)
- [Utilizing Adversarial Examples for Bias Mitigation and Accuracy Enhancement](https://mlsanity.com/paper/2404.11819/) (2024)
- [Fair Bayesian Model-Based Clustering](https://mlsanity.com/paper/2506.12839/) (2025)
- [Uncover and Unlearn Nuisances: Agnostic Fully Test-Time Adaptation](https://mlsanity.com/paper/2511.12491/) (2025)
- [Interpretable Fair Clustering](https://mlsanity.com/paper/2511.21109/) (2025)
- [Fairness risk and its privacy-enabled solution in AI-driven robotic applications](https://mlsanity.com/paper/2601.08953/) (2026)
- [Fair Model-based Clustering](https://mlsanity.com/paper/2602.21509/) (2026)
- [Coordinated Disentanglement with Iterative Mode Discovery Under Hidden Correlations](https://mlsanity.com/paper/2607.17264/) (2026)
- [COVAriance-Induced Fairness Gap Penalty for Subgroup-Fair Clustering](https://mlsanity.com/paper/2607.18119/) (2026)

## Abstract (arXiv)

Fair clustering aims to divide data into distinct clusters while preventing sensitive attributes (textite.g., gender, race, RNA sequencing technique) from dominating the clustering. Although a number of works have been conducted and achieved huge success recently, most of them are heuristical, and there lacks a unified theory for algorithm design. In this work, we fill this blank by developing a mutual information theory for deep fair clustering and accordingly designing a novel algorithm, dubbed FCMI. In brief, through maximizing and minimizing mutual information, FCMI is designed to achieve four characteristics highly expected by deep fair clustering, textiti.e., compact, balanced, and fair clusters, as well as informative features. Besides the contributions to theory and algorithm, another contribution of this work is proposing a novel fair clustering metric built upon information theory as well. Unlike existing evaluation metrics, our metric measures the clustering quality and fairness as a whole instead of separate manner. To verify the effectiveness of the proposed FCMI, we conduct experiments on six benchmarks including a single-cell RNA-seq atlas compared with 11 state-of-the-art methods in terms of five metrics. The code could be accessed from url https://pengxi.me.