Hierarchical and Fast Graph Similarity Computation via Graph Coarsening and Deep Graph Learning
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In this work, we are interested in the large graph similarity computation problem, which is one of the most important graph-based problems. Traditional techniques to compute the exact or approximate values of Graph Edit Distance (GED) and Maximum Common Subgraph (MCS) require at least polynomial time complexity over node numbers thus are not able to handle this problem when the numbers of nodes are large. Recently the develop of deep learning techniques provide a promising solution for this problem by training a network which is able to encode graphs to feature vectors and then compute similarity based on feature vectors. However, when we look into these techniques and classify them to embedding models and matching models, problems arise. Embedding models can be quite fast but perform poorly due to the lack of interaction across graphs while matching models involve this for much better performance but satisfy far more on time consumption. Similar to the process of large biological molecular identification, where we first maps the whole molecular to molecular groups and then identify them based on the "abstracted smaller molecular", the feature aggregation across two whole graphs is always redundant, especially when the number of nodes is large. Thus we here present a novel framework for large graph similarity computation problem. We first embed and coarsen the large graphs to "abstracted smaller graphs" with denser local topology, similar to molecular groups in biological concept. Then we aggregate both the internal features in "abstracted smaller graphs" and external features across "abstracted smaller graph pair", leading to feature vectors for each graph, with which we calculate the final similarity score. Experiments demonstrate that our proposed framework outperforms state-of-the-art methods in graph similarity computation tasks and has significant improvement in time efficiency.
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