论文标题
在线性融合的Gromov-Wasserstein距离上，用于图形结构化数据
On a linear fused Gromov-Wasserstein distance for graph structured data
论文作者
论文摘要
我们提出了一个将图形结构化数据嵌入向量空间中的框架，考虑到图形的节点特征和拓扑结构，并将其嵌入到最佳传输（OT）问题中。然后，我们提出了两个图表之间的新距离，称为LinearFGW，定义为它们的嵌入之间的欧几里得距离。提出的距离的优点是双重的：1）它可以考虑到基于内核的框架中图形相似性的节点特征和图表的结构，2）对于计算基于成对的OT的距离（尤其是融合的gromov-wasseant），它可能要快得多，尤其是与基于成对的ot的距离，可以处理大型数据集。在讨论了线性性的理论特性之后，我们在分类和聚类任务上展示了实验结果，显示了所提出的线性线性的有效性。
We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named linearFGW, defined as the Euclidean distance between their embeddings. The advantages of the proposed distance are twofold: 1) it can take into account node feature and structure of graphs for measuring the similarity between graphs in a kernel-based framework, 2) it can be much faster for computing kernel matrix than pairwise OT-based distances, particularly fused Gromov-Wasserstein, making it possible to deal with large-scale data sets. After discussing theoretical properties of linearFGW, we demonstrate experimental results on classification and clustering tasks, showing the effectiveness of the proposed linearFGW.
