COPT：图形绘制的协调最优传输
COPT: Coordinated Optimal Transport for Graph Sketching
摘要：
我们引入COPT，通过优化程序定义的图形之间的一种新的距离度量，同时计算一对协调的最佳运输地图。这提供了一种无监督的方式来学习通用图形表示，适用于图形草图和图形比较。COPT涉及同时优化双重运输计划，一个在两个图的顶点之间，另一个在图信号概率分布之间。我们从理论上表明，我们的方法保留了重要的全局结构信息的图形，特别是光谱信息，并分析连接到现有的研究。从经验上讲，COPT在合成和真实数据集上的图分类中优于最先进的方法。
英文摘要：
We introduce COPT, a novel distance metric between graphs defined via an optimization routine, computing a coordinated pair of optimal transport maps simultaneously. This gives an unsupervised way to learn general-purpose graph representation, applicable to both graph sketching and graph comparison. COPT involves simultaneously optimizing dual transport plans, one between the vertices of two graphs, and another between graph signal probability distributions. We show theoretically that our method preserves important global structural information on graphs, in particular spectral information, and analyze connections to existing studies. Empirically, COPT outperforms state of the art methods in graph classification on both synthetic and real datasets.
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