More Interpretable Graph Similarity Computation via Maximum Common Subgraph Inference

Graph similarity measurement, which computes the distance/similarity between two graphs, arises in various graph-related tasks. Recent learning-based methods lack interpretability, as they directly transform interaction information between two graphs into one hidden vector and then map it to similarity. To cope with this problem, this study proposes a more interpretable end-to-end paradigm for graph similarity learning, named Similarity Computation via Maximum Common Subgraph Inference (INFMCS). Our critical insight into INFMCS is the strong correlation between similarity score and Maximum Common Subgraph (MCS). We implicitly infer MCS to obtain the normalized MCS size, with the supervision information being only the similarity score during training. To capture more global information, we also stack some vanilla transformer encoder layers with graph convolution layers and propose a novel permutation-invariant node Positional Encoding. The entire model is quite simple yet effective. Comprehensive experiments demonstrate that INFMCS consistently outperforms state-of-the-art baselines for graph-graph classification and regression tasks. Ablation experiments verify the effectiveness of the proposed computation paradigm and other components. Also, visualization and statistics of results reveal the interpretability of INFMCS.