提出可调公平性与效果平衡的深度图聚类方法，提升敏感群体代表性。
A Deep Latent Factor Graph Clustering with Fairness-Utility Trade-off Perspective
- 基于深度非负三因子分解，端到端优化聚类分配
- 单一参数控制公平性与性能权衡，保持高群组平衡
- 适用于社区发现、资源分配等需公平性的场景
公平图聚类旨在划分网络结构的同时保障敏感群体的合理代表，应用涵盖社区发现、团队组建、资源分配与社交网络分析。现有方法多依赖刚性约束或多阶段流程（如谱嵌入后接k-means），限制了权衡控制、可解释性与可扩展性。本文提出DFNMF，一种面向图的端到端深度非负三因子分解方法，直接优化聚类分配并引入软统计均等性正则项。仅通过一个参数λ调节公平性-效用平衡，非负性带来部件式因子与透明的软隶属关系。优化采用稀疏友好交替更新，计算复杂度近线性于边数。在合成与真实网络上，DFNMF在相近模块度下显著提升群组平衡性，多数情况下优于当前最优基线，在帕累托前沿表现更优。代码已公开于https://github.com/SiamakGhodsi/DFNMF.git。
原文摘要 · Abstract (English)
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.
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