Matching node embeddings for graph similarity

Graph kernels have emerged as a powerful tool for graph comparison. Most existing graph kernels focus on local properties of graphs and ignore global structure. In this paper, we compare graphs based on their global properties as these are captured by the eigenvectors of their adjacency matrices. We present two algorithms for both labeled and unlabeled graph comparison. These algorithms represent each graph as a set of vectors corresponding to the embeddings of its vertices. The similarity between two graphs is then determined using the Earth Mover's Distance metric. These similarities do not yield a positive semidefinite matrix. To address for this, we employ an algorithm for SVM classification using indefinite kernels. We also present a graph kernel based on the Pyramid Match kernel that finds an approximate correspondence between the sets of vectors of the two graphs. We further improve the proposed kernel using the Weisfeiler-Lehman framework. We evaluate the proposed methods on several benchmark datasets for graph classification and compare their performance to state-of-the-art graph kernels. In most cases, the proposed algorithms outperform the competing methods, while their time complexity remains very attractive.