# A Unified Framework for Fair Spectral Clustering With Effective Graph Learning

arXiv: https://arxiv.org/abs/2311.13766 · HTML: https://mlsanity.com/paper/2311.13766/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 60 references that are in the map.
- First posted on arXiv 23 Nov 2023.

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

- [Fair Clustering Through Fairlets](https://mlsanity.com/paper/1802.05733/) (2018)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [The Frontiers of Fairness in Machine Learning](https://mlsanity.com/paper/1810.08810/) (2018)
- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Fair Algorithms for Clustering](https://mlsanity.com/paper/1901.02393/) (2019)
- [Collaborative Deep Learning for Recommender Systems](https://mlsanity.com/paper/1409.2944/) (2014)
- [Scalable Fair Clustering](https://mlsanity.com/paper/1902.03519/) (2019)
- [Multi-view Contrastive Graph Clustering](https://mlsanity.com/paper/2110.11842/) (2021)
- [Guarantees for Spectral Clustering with Fairness Constraints](https://mlsanity.com/paper/1901.08668/) (2019)
- [A Unified Framework for Structured Graph Learning via Spectral Constraints](https://mlsanity.com/paper/1904.09792/) (2019)
- [Label Efficient Semi-Supervised Learning via Graph Filtering](https://mlsanity.com/paper/1901.09993/) (2019)
- [Large Scale Graph Learning from Smooth Signals](https://mlsanity.com/paper/1710.05654/) (2017)
- [Deep Fair Clustering via Maximizing and Minimizing Mutual Information: Theory, Algorithm and Metric](https://mlsanity.com/paper/2209.12396/) (2022)
- [Accelerated Graph Learning from Smooth Signals](https://mlsanity.com/paper/2110.09677/) (2021)
- [Scalable Spectral Clustering with Group Fairness Constraints](https://mlsanity.com/paper/2210.16435/) (2022)
- [Twin Learning for Similarity and Clustering: A Unified Kernel Approach](https://mlsanity.com/paper/1705.00678/) (2017)
- [Unified Spectral Clustering with Optimal Graph](https://mlsanity.com/paper/1711.04258/) (2017)
- [Fair Community Detection and Structure Learning in Heterogeneous Graphical Models](https://mlsanity.com/paper/2112.05128/) (2021)
- [Hierarchical Clustering Supported by Reciprocal Nearest Neighbors](https://mlsanity.com/paper/1907.04915/) (2019)
- [Graph Tikhonov Regularization and Interpolation via Random Spanning Forests](https://mlsanity.com/paper/2011.10450/) (2020)
- [Discrete Optimal Graph Clustering](https://mlsanity.com/paper/1904.11266/) (2019)
- [Spectral Normalized-Cut Graph Partitioning with Fairness Constraints](https://mlsanity.com/paper/2307.12065/) (2023)

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

- [Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior](https://mlsanity.com/paper/2406.09513/) (2024)
- [Fairness-Aware Estimation of Graphical Models](https://mlsanity.com/paper/2408.17396/) (2024)
- [Estimating Fair Graphs from Graph-Stationary Data](https://mlsanity.com/paper/2510.07536/) (2025)

## Abstract (arXiv)

We consider the problem of spectral clustering under group fairness constraints, where samples from each sensitive group are approximately proportionally represented in each cluster. Traditional fair spectral clustering (FSC) methods consist of two consecutive stages, i.e., performing fair spectral embedding on a given graph and conducting kmeans to obtain discrete cluster labels. However, in practice, the graph is usually unknown, and we need to construct the underlying graph from potentially noisy data, the quality of which inevitably affects subsequent fair clustering performance. Furthermore, performing FSC through separate steps breaks the connections among these steps, leading to suboptimal results. To this end, we first theoretically analyze the effect of the constructed graph on FSC. Motivated by the analysis, we propose a novel graph construction method with a node-adaptive graph filter to learn graphs from noisy data. Then, all independent stages of conventional FSC are integrated into a single objective function, forming an end-to-end framework that inputs raw data and outputs discrete cluster labels. An algorithm is developed to jointly and alternately update the variables in each stage. Finally, we conduct extensive experiments on synthetic, benchmark, and real data, which show that our model is superior to state-of-the-art fair clustering methods.