The PWLR Graph Representation: A Persistent Weisfeiler-Lehman scheme with Random Walks for Graph Classification
This addresses the problem of graph classification for researchers and practitioners, offering a novel framework that generalizes existing methods, though it appears incremental in combining known techniques.
The paper tackles graph classification by introducing the PWLR scheme, which integrates Weisfeiler-Lehman procedures, random walks, and persistent homology to create explainable low-dimensional representations; it achieves comparable results to state-of-the-art methods for graphs with discrete node labels and enhanced performances for those with continuous features.
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.