Hierarchical Abstracting Graph Kernel

Graph kernels have been regarded as a successful tool for handling a variety of graph applications since they were proposed. However, most of the proposed graph kernels are based on the R-convolution framework, which decomposes graphs into a set of substructures at the same abstraction level and compares all substructure pairs equally; these methods inherently overlook the utility of the hierarchical structural information embedded in graphs. In this paper, we propose H ierarchical A bstracting G raph K ernels (HAGK), a novel set of graph kernels that compare graphs’ hierarchical substructures to capture and utilize the latent hierarchical structural information fully. Instead of generating non-structural substructures, we reveal each graph’s hierarchical substructures by constructing its hierarchical abstracting , specifically, the hierarchically organized nested node sets adhering to the principle of structural entropy minimization. To compare a pair of hierarchical abstractings, we propose two novel substructure matching approaches, Local Optimal Matching (LOM) and Priority Ordering Matching (POM), to find appropriate matching between the substructures by different strategies recursively. Extensive experiments demonstrate that the proposed kernels are highly competitive with the existing state-of-the-art graph kernels, and verify that the hierarchical abstracting plays a significant role in the improvement of the kernel performance.