Graph matching finds the correspondence of nodes across two graphs and is a basic task in graph-based machine learning. Numerous existing methods match every node in one graph to one node in the other graph whereas two graphs usually overlap partially in many \realworld{} applications. In this paper, a partial Gromov-Wasserstein learning framework is proposed for partially matching two graphs, which fuses the partial Gromov-Wasserstein distance and the partial Wasserstein distance as the objective and updates the partial transport map and the node embedding in an alternating fashion. The proposed framework transports a fraction of the probability mass and matches node pairs with high relative similarities across the two graphs. Incorporating an embedding learning method, heterogeneous graphs can also be matched. Numerical experiments on both synthetic and \realworld{} graphs demonstrate that our framework can improve the F1 score by at least $20\%$ and often much more.

翻译：图表匹配两个图形的节点对应, 是基于图形的机器学习的基本任务。 许多现有方法将一个图形中的每个节点匹配到另一个图形中的每个节点, 而两个图表通常在许多\ realworld\\\\\ 应用程序中部分重叠。 在本文中, 为部分匹配两个图表建议了一个部分的 Gromov- Wasserstein 学习框架, 将部分格罗莫夫- Wasserstein 距离和部分瓦塞尔斯坦 距离连接起来, 作为目标, 并更新部分运输地图和节点以交替方式嵌入。 拟议的框架将概率质量的一小部分与两个图表中具有高度相对相似性的节点匹配。 包含嵌入学习方法, 混杂图形也可以匹配。 合成和现实世界的数值实验显示, 我们的框架可以提高F1的得分至少20 ⁇ 美元, 并且往往更多。