论文标题
基于运输的图形内核
Transport based Graph Kernels
论文作者
论文摘要
Graph内核是一种强大的工具，可测量图形之间的相似性。大多数现有的图形内核都集中在节点标签或属性上，并忽略了图层次结构信息。为了有效利用图形层次结构信息，我们建议基于最佳传输（OT）的金字塔图内核。每个图都嵌入金字塔的分层结构中。然后，使用OT距离来测量层次结构中图之间的相似性。我们还利用OT距离来测量子图之间的相似性，并基于OT提出子图内核。基于最佳传输距离的图内的阳性半芬矿（P.S.D）不一定是可能的。我们进一步提出了基于OT的正则图内核，在该图中我们将内核正则化添加到原始的最佳传输距离中以获得P.S.D内核矩阵。我们在几个基准分类任务上评估了所提出的图形内核，并将其性能与现有的最新图形内核进行比较。在大多数情况下，我们提出的图表内核算法的表现优于竞争方法。
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph hierarchical structure information, we propose pyramid graph kernel based on optimal transport (OT). Each graph is embedded into hierarchical structures of the pyramid. Then, the OT distance is utilized to measure the similarity between graphs in hierarchical structures. We also utilize the OT distance to measure the similarity between subgraphs and propose subgraph kernel based on OT. The positive semidefinite (p.s.d) of graph kernels based on optimal transport distance is not necessarily possible. We further propose regularized graph kernel based on OT where we add the kernel regularization to the original optimal transport distance to obtain p.s.d kernel matrix. We evaluate the proposed graph kernels on several benchmark classification tasks and compare their performance with the existing state-of-the-art graph kernels. In most cases, our proposed graph kernel algorithms outperform the competing methods.
