用最优传输比较网络，能算差距还能看节点如何变化。
Optimal Transport for Network Comparison: A Review with Machine Learning Applications
- 用三种传输距离衡量无向无权图差异，同时生成节点转移路径。
- 实验证明在聚类和异常检测任务中优于传统图指标。
- 可快速估算谱距离，适合大规模网络分析，适合图学习研究者。
基于最优传输的网络比较是网络科学中的新兴研究方向。与传统图度量不同，最优传输不仅能计算图间差异，还能生成一个传输计划，揭示一个图如何转化为另一个图。本文综述了三种主要距离：Wasserstein、Gromov-Wasserstein 和 Bures-Wasserstein 距离，用于比较无向、无权图。通过节点特征概率分布的闭式解，推导了一维情况下的 Wasserstein 距离；并证明 Wasserstein 与 Gromov-Wasserstein 的传输计划能捕捉图扰动后影响距离的关键节点。针对 Bures-Wasserstein 距离，利用拉普拉斯谱导出上下界，避免完整谱分解。最后，在合成网络数据集上进行聚类评估，并在真实时间序列网络上实现异常检测，验证了方法的有效性。
原文摘要 · Abstract (English)
Network comparison using optimal transport is a growing area of research in network science. Unlike standard graph metrics, optimal transport computes both network dissimilarity and a transport plan that explains how one graph morphs into another. In this paper, we review how optimal transport compares undirected, unweighted graphs using three primary distances: the Wasserstein, Gromov-Wasserstein, and Bures-Wasserstein distances. We examine the closed form of the Wasserstein distance in one dimension via node feature probability distributions, and show how the transport plans of the Wasserstein and Gromov-Wasserstein distances capture which specific nodes influence the distance after graph perturbation. For the Bures-Wasserstein distance, we derive bounds using Laplacian spectra to bypass full spectral decompositions. Finally, we evaluate these distances using a synthetic network dataset for clustering and a real-world time series network for anomaly detection.
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