用于网络比较的最优传输：面向机器学习应用的综述
Optimal Transport for Network Comparison: A Unified Review with New Spectral Bounds and Machine Learning Applications
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中文总结 AI 辅助
该综述介绍了Wasserstein等三种最优传输距离用于无向无权图比较的方法，推导了相关闭式形式与界，并在聚类和异常检测任务中验证了其应用效果。
中文摘要 AI 辅助
利用最优传输进行网络比较是网络科学中一个新兴的研究领域。与标准图度量不同，最优传输可同时计算网络的不相似性及解释一个图如何演变为另一个图的传输计划。本文综述了最优传输如何通过三种主要距离比较无向无权图，即Wasserstein距离、Gromov-Wasserstein距离和Bures-Wasserstein距离；研究了一维Wasserstein距离通过节点特征概率分布的闭式形式，证明了Wasserstein和Gromov-Wasserstein距离的传输计划可捕捉图扰动后影响距离的特定节点；针对Bures-Wasserstein距离，推导了基于拉普拉斯谱的界以规避全谱分解；最后，采用合成网络数据集开展聚类评估，采用真实世界时间序列网络开展异常检测评估。
英文摘要
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 simple 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 visualize how mass is shifted to transform one network into another. Beyond reviewing existing transport-based approaches, we establish new spectral lower and upper bounds for the Bures-Wasserstein distance and characterize the tightness of the lower bound under eigenbasis perturbations. Finally, we evaluate these distances using a synthetic network dataset for clustering and a real-world temporal network.
