Deep Hierarchical Graph Alignment Kernels
This work addresses a limitation in graph kernel methods for machine learning tasks involving graph data, representing an incremental improvement over existing approaches.
The paper tackles the problem of graph kernels overlooking implicit similarities and topological positions of substructures by introducing Deep Hierarchical Graph Alignment Kernels (DHGAK), which hierarchically align relational substructures in an embedding space and demonstrate effectiveness and efficiency on benchmark datasets.
Typical R-convolution graph kernels invoke the kernel functions that decompose graphs into non-isomorphic substructures and compare them. However, overlooking implicit similarities and topological position information between those substructures limits their performances. In this paper, we introduce Deep Hierarchical Graph Alignment Kernels (DHGAK) to resolve this problem. Specifically, the relational substructures are hierarchically aligned to cluster distributions in their deep embedding space. The substructures belonging to the same cluster are assigned the same feature map in the Reproducing Kernel Hilbert Space (RKHS), where graph feature maps are derived by kernel mean embedding. Theoretical analysis guarantees that DHGAK is positive semi-definite and has linear separability in the RKHS. Comparison with state-of-the-art graph kernels on various benchmark datasets demonstrates the effectiveness and efficiency of DHGAK. The code is available at Github (https://github.com/EWesternRa/DHGAK).