This paper presents the Persistent Weisfeiler-Lehman Random walk scheme (abbreviated as PWLR) for graph representations, a novel mathematical framework which produces a collection of explainable low-dimensional representations of graphs with discrete and continuous node features. The proposed scheme effectively incorporates normalized Weisfeiler-Lehman procedure, random walks on graphs, and persistent homology. We thereby integrate three distinct properties of graphs, which are local topological features, node degrees, and global topological invariants, while preserving stability from graph perturbations. This generalizes many variants of Weisfeiler-Lehman procedures, which are primarily used to embed graphs with discrete node labels. Empirical results suggest that these representations can be efficiently utilized to produce comparable results to state-of-the-art techniques in classifying graphs with discrete node labels, and enhanced performances in classifying those with continuous node features.
翻译:本文展示了用于图形表达的“持久Weisfeiler-Lehman随机行走计划”(作为PWLR的缩写),这是一个创新的数学框架,它汇集了可解释的低维显示具有离散和连续节点特点的图形。拟议方案有效地纳入了标准化 Weisfeiler-Lehman程序、图上随机行走和持久性同质学。因此,我们整合了三个不同的图形特性,它们是局部的地貌特征、节点度和全球地貌异质,同时保持了图突扰的稳定性。这概括了Weisfeiler-Lehman程序的许多变量,主要用于嵌入带有离散节点标签的图形。经验性结果表明,这些特征可以高效地用于产生可与离散节点标签的图表分类最新技术相匹配的结果,并提高了对具有连续节点特征的图形进行分类的性能。