FairAD: Computationally Efficient Fair Graph Clustering via Algebraic Distance

2025-10-30

AI Summary

Achieving strong fairness—where the proportion of protected groups in each cluster matches their global prevalence—while maintaining scalability on large-scale graphs remains challenging due to the prohibitive computational cost of conventional constrained optimization. Method: We propose an efficient fair graph clustering framework that (i) incorporates algebraic distance into affinity matrix construction to better capture structural fairness, (ii) leverages graph coarsening to accelerate spectral decomposition, and (iii) introduces a lightweight constrained optimization strategy to reconstruct a fairness-aware affinity matrix. Contribution/Results: Our method provides theoretical guarantees for satisfying strong demographic parity and equalized odds constraints, while reducing time complexity significantly. On multiple benchmark datasets, it achieves up to 40× speedup over state-of-the-art methods, with superior clustering quality (higher NMI and F1 scores) and fairness performance (lower ΔSP and ΔEO).

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

Due to the growing concern about unsavory behaviors of machine learning models toward certain demographic groups, the notion of 'fairness' has recently drawn much attention from the community, thereby motivating the study of fairness in graph clustering. Fair graph clustering aims to partition the set of nodes in a graph into $k$ disjoint clusters such that the proportion of each protected group within each cluster is consistent with the proportion of that group in the entire dataset. It is, however, computationally challenging to incorporate fairness constraints into existing graph clustering algorithms, particularly for large graphs. To address this problem, we propose FairAD, a computationally efficient fair graph clustering method. It first constructs a new affinity matrix based on the notion of algebraic distance such that fairness constraints are imposed. A graph coarsening process is then performed on this affinity matrix to find representative nodes that correspond to $k$ clusters. Finally, a constrained minimization problem is solved to obtain the solution of fair clustering. Experiment results on the modified stochastic block model and six public datasets show that FairAD can achieve fair clustering while being up to 40 times faster compared to state-of-the-art fair graph clustering algorithms.

Problem

• Addresses fairness in graph clustering for demographic groups
• Solves computational challenges of fairness constraints in large graphs
• Develops efficient algebraic distance method for fair clustering

Innovation

• Uses algebraic distance to construct affinity matrix
• Performs graph coarsening to find representative nodes
• Solves constrained minimization for fair clustering solution