The ability to compute similarity scores between graphs based on metrics such as Graph Edit Distance (GED) is important in many real-world applications, such as 3D action recognition and biological molecular identification. Computing exact GED values is typically an NP-hard problem and traditional algorithms usually achieve an unsatisfactory trade-off between accuracy and efficiency. Recently, Graph Neural Networks (GNNs) provide a data-driven solution for this task, which is more efficient while maintaining prediction accuracy in small graph (around 10 nodes per graph) similarity computation. Existing GNN-based methods, which either respectively embed two graphs (lack of low-level cross-graph interactions) or deploy cross-graph interactions for whole graph pairs (redundant and time-consuming), are still not able to achieve competitive results when the number of nodes in graphs increases. In this paper, we focus on similarity computation for large-scale graphs and propose the embedding-coarsening-matching framework, which first embeds and coarsens large graphs to coarsened graphs with denser local topology and then deploys fine-grained interactions on the coarsened graphs for the final similarity scores.
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