Graph Structure Similarity Method using Mass-controlled Optimal Transport

Abstract

There are two crucial points in comparing graph structures. One is the representation of node feature vectors, and the other is the extraction of essential substructures. The representation of node feature vectors in graphs has been actively studied in graph representation learning to construct Graph Neural Networks (GNNs) that outperform the Weisfeiler-Lehman (WL) test. On the other hand, the latter is often used as a criterion for graph classification tasks, and comparison between key substructures is significant when comparing structures. However, the extraction of key structures is a difficult task and has not been sufficiently studied. In this paper, instead of extracting the key structures directly, we compare the structures that are likely to be important by giving weights to similar structures. Furthermore, we define a new distance between graphs. The results of the graph classification task using k-NN show that the proposed method outperforms the traditional distance methods.