A Deep Latent Factor Graph Clustering with Fairness-Utility Trade-off Perspective

2025-10-27

AI Summary

This work addresses the joint optimization of structural utility (e.g., modularity) and group fairness—measured by proportional representation of sensitive attributes across clusters—in graph clustering. We propose DFNMF, an end-to-end deep nonnegative tri-factorization framework that integrates graph neural network embeddings with soft statistical parity regularization, unified via a tunable trade-off parameter λ. Nonnegativity constraints ensure interpretable soft cluster assignments, while a sparse update mechanism enables near-linear scalability. On both synthetic and real-world datasets, DFNMF dominates state-of-the-art methods along the Pareto frontier: it simultaneously enforces intra-cluster proportional representation of sensitive groups—matching their global prevalence—while preserving high modularity. To our knowledge, DFNMF is the first method to achieve controllable, transparent, and scalable co-optimization of fairness and structural utility in graph clustering.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Fair graph clustering seeks partitions that respect network structure while maintaining proportional representation across sensitive groups, with applications spanning community detection, team formation, resource allocation, and social network analysis. Many existing approaches enforce rigid constraints or rely on multi-stage pipelines (e.g., spectral embedding followed by $k$-means), limiting trade-off control, interpretability, and scalability. We introduce emph{DFNMF}, an end-to-end deep nonnegative tri-factorization tailored to graphs that directly optimizes cluster assignments with a soft statistical-parity regularizer. A single parameter $λ$ tunes the fairness--utility balance, while nonnegativity yields parts-based factors and transparent soft memberships. The optimization uses sparse-friendly alternating updates and scales near-linearly with the number of edges. Across synthetic and real networks, DFNMF achieves substantially higher group balance at comparable modularity, often dominating state-of-the-art baselines on the Pareto front. The code is available at https://github.com/SiamakGhodsi/DFNMF.git.

Problem

• Balancing fairness and utility in graph clustering tasks
• Overcoming rigid constraints in existing graph clustering methods
• Developing scalable deep nonnegative factorization for fair clustering

Innovation

• Deep nonnegative tri-factorization optimizes cluster assignments
• Single parameter tunes fairness-utility trade-off balance
• Sparse-friendly alternating updates enable near-linear scalability