用曲率引导扩散，无监督发现异质图社区结构。
Curvature-Guided Sheaf Diffusion for Unsupervised Community Detection on Heterophilic Graphs
- 以边的离散曲率为拓扑信号，全程驱动无监督社区检测。
- 在威斯康星和查梅莱翁数据集上表现最佳，提升15%准确率。
- 方法可解释性强，适合研究图结构与社区关系的学者。
在异质图中，连接节点常属不同类别，传统无监督社区检测方法难以应对：经典模块度与谱方法不依赖特征，而深度图聚类方法依赖对比或生成机制，缺乏透明性。本文提出曲率引导流扩散（CGSD），一种全无监督社区检测算法，仅使用每条边的离散Forman-Ricci曲率作为唯一拓扑信号，并贯穿整个端到端流程。主要贡献包括：(i) 基于曲率门控的流扩散编码器，通过σ(κ_e)调控边消息，训练基于三种无标签结构损失（模块度、反坍塌、曲率加权重构）；(ii) 曲率感知谱聚类器（CSpec），在Ng-Jordan-Weiss前用σ(ακ_{e^*})重加权k-NN邻接矩阵；(iii) 对九种真正无监督基线的统一无标签评估。在五个异质图基准（Cora, Cornell, Texas, Wisconsin, Chameleon）上，CGSD在Wisconsin和Chameleon上胜出，在其余三个上也具竞争力。性能提升主要来自聚类器：同一嵌入下，CSpec使平均NMI从0.091（K-Means）提升至0.107（+15%，配对t检验p=0.008）。机制可解释：社区内与社区间曲率分布明显分离。代码已开源：https://github.com/woodywff/cgsd。
原文摘要 · Abstract (English)
Detecting communities in heterophilic graphs -- where connected nodes often belong to different classes -- is hard for unsupervised methods: classical modularity and spectral methods are feature agnostic, while deep graph-clustering methods rely on contrastive or generative machinery that is opaque. We propose Curvature-Guided Sheaf Diffusion (CGSD), a fully unsupervised community-detection algorithm that uses the discrete Forman--Ricci curvature of each edge as its single topological signal, propagated through every stage of an end-to-end pipeline. CGSD makes three concrete contributions: (i)~a curvature-gated sheaf-diffusion encoder that gates edge messages by $σ(κ_e)$ and is trained from three label-free structural losses (modularity, anti-collapse, curvature-weighted reconstruction); (ii)~a curvature-aware spectral clusterer (CSpec) that re-weights the $k$-NN affinity of the embedding by $σ(ακ_{e^*})$ before Ng--Jordan--Weiss; and (iii)~a unified label-free evaluation against nine truly-unsupervised baselines. On five heterophilic benchmarks (Cora, Cornell, Texas, Wisconsin, Chameleon), CGSD wins outright on Wisconsin and Chameleon and is competitive on the remaining three against nine unsupervised baselines. The gain over the strongest baseline is driven by the clusterer, not the encoder: on the same embedding, CSpec improves mean NMI from $0.091$ with $K$-Means to $0.107$ ($+15\%$, paired $t$-test $p=0.008$). The mechanism is interpretable: intra-community and inter-community curvature distributions are visibly separated. Code is open-sourced at https://github.com/woodywff/cgsd.
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