论文标题
COPT：协调图形草图的最佳运输
COPT: Coordinated Optimal Transport for Graph Sketching
论文作者
论文摘要
我们介绍了COPT，这是通过优化例程定义的图表之间的新型距离度量，同时计算了一对配位的最佳传输映射。这提供了一种无监督的方法来学习通用图表表示，适用于图形草图和图形比较。 COPT涉及同时优化双传输计划，一个在两个图的顶点之间，另一个之间是图形信号概率分布之间。从理论上讲，我们的方法保留了有关图的重要全球结构信息，特别是光谱信息，并分析了与现有研究的联系。从经验上讲，在合成数据集和真实数据集上，COPT在图形分类中优于ART方法的状态。
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.
