Beyond Histogram Comparison: Distribution-Aware Simple-Path Graph Kernels

R-convolution graph kernels are conventional methods for graph classification. They decompose graphs into substructures and aggregate all the substructure similarity as graph similarity. However, the substructure similarity is based on graph isomorphism, which not only leads to binary similarity values but also cannot be aware of the probability distribution of substructures in each graph. Moreover, the simple sum aggregation is not aware of the probability distribution differences of substructures across graphs. These drawbacks cause inaccurate graph similarity. To resolve these problems, we propose a new method called the distribution-aware simple-path (DASP) graph kernel. The neural language models are employed to capture the probability distribution of substructures (specifically, simple paths) in each graph. A new metric called probabilistic Minkowski distance is developed to capture the probability distribution differences of simple paths across graphs. To further improve the performance, the label alphabet is expanded to enlarge the corpus of simple paths for the neural language models and DASP. Experiments demonstrate that DASP achieves the best classification accuracy on all the selected graph benchmark datasets.