发表机构
Syracuse University（雪城大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对边采样中局部编辑难以控制全局结构的问题，提出基于谱矩的采样框架，通过组合与低秩方法高效计算矩变化，证明矩保持可保留结构属性并改进图学习。
AI 中文摘要
边采样通过局部决策来实现图级目标，例如保持结构属性。这带来了一个根本性挑战：\textit{如何量化和控制局部边编辑（即边的添加或移除）对全局图结构的影响？}我们通过一个基于随机游走转移矩阵的谱矩的\textit{矩引导边采样框架}来解决这一挑战。我们通过两种互补的方法计算精确的矩变化：一种组合方法，对低阶矩提供闭式更新；以及一种低秩方法，利用\textit{局部性}和\textit{循环迹不变性}将计算压缩到被编辑的端点，支持任意矩阶和批量编辑。对于固定矩阶的单边编辑，低秩方法将成本从$O(mn)$降低到$O(m)$，而组合方法在维护局部统计信息的情况下，以常数时间评估低阶变化。这些矩变化提供了\textbf{可解释的结构签名}，用于局部边模体，这些模体聚合成图级指纹。这种结构意义促使我们思考：保持矩是否也能保持图属性。我们进一步推导并验证，保持矩的采样能够\textbf{保留相关的结构属性}，包括三角形加权聚类系数。这些结构洞见使得\textbf{分析和改进图学习}成为可能：不同的边结构对监督节点分类有不同的影响，而矩引导增强在图对比学习中具有竞争力。总之，这些发现确立了矩作为从局部边编辑到全局图结构和学习的可解释且可控的桥梁。
英文摘要
Edge sampling makes local decisions to achieve graph-level objectives, such as preserving structural properties. This creates a fundamental challenge: \textit{how can the effect of a local edge edit (i.e., edge addition or removal) on global graph structure be quantified and controlled?} We address this challenge with a \textit{moment-guided edge sampling framework} based on spectral moments of the random-walk transition matrix. We compute exact moment changes through two complementary methods: a combinatorial method with closed-form updates for low-order moments, and a low-rank method that exploits \textit{locality} and \textit{cyclic trace invariance} to compress computations to edited endpoints, supporting arbitrary moment orders and batched edits. For single-edge edits at fixed moment orders, the low-rank method reduces the cost from $O(mn)$ to $O(m)$, while the combinatorial method evaluates low-order changes in constant time given maintained local statistics. These moment changes provide \textbf{interpretable structural signatures} of local edge motifs that aggregate into graph-level fingerprints. This structural meaning motivates us to ask whether preserving moments also preserves the graph properties. We further derive and validate that moment-preserving sampling can \textbf{retain related structural properties}, including triangle-weighted clustering coefficient. These structural insights enable \textbf{analysis and improvement of graph learning}: different edge structures have distinct effects on supervised node classification, while moment-guided augmentation is competitive for graph contrastive learning. Together, these findings establish moments as an interpretable and controllable bridge from local edge edits to global graph structure and learning.
CommentsCode: https://github.com/Weibin44/Moment-guided-graph-sampling
