Interpretable Graph Similarity Computation via Differentiable Optimal Alignment of Node Embeddings

Computing graph similarity is an important task in many graph-related applications such as retrieval in graph databases or graph clustering. While numerous measures have been proposed to capture the similarity between a pair of graphs, Graph Edit Distance (GED) and Maximum Common Subgraphs (MCS) are the two widely used measures in practice. GED and MCS are domain-agnostic measures of structural similarity between the graphs and define the similarity as a function of pairwise alignment of different entities (such as nodes, edges, and subgraphs) in the two graphs. The explicit explainability offered by the pairwise alignment provides transparency and justification of the similarity score, thus, GED and MCS have important practical applications. However, their exact computations are known to be NP-hard. While recently proposed neural-network based approximations have been shown to accurately compute these similarity scores, they have limited ability in providing comprehensive explanations compared to classical combinatorial algorithms, e.g., Beam search. This paper aims at efficiently approximating these domain-agnostic similarity measures through a neural network, and simultaneously learning the alignments (i.e., explanations) similar to those of classical intractable methods. Specifically, we formulate the similarity between a pair of graphs as the minimal "transformation" cost from one graph to another in the learnable node-embedding space. We show that, if node embedding is able to capture its neighborhood context closely, our proposed similarity function closely approximates both the alignment and the similarity score of classical methods. Furthermore, we also propose an efficient differentiable computation of our proposed objective for model training. Empirically, we demonstrate that the proposed method achieves up to 50%-100% reduction in the Mean Squared Error for the graph similarity approximation task and up to 20% improvement in the retrieval evaluation metrics for the graph retrieval task. The source code is available at https://github.com/khoadoan/GraphOTSim.