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).

通过深层次图对齐核（Deep Hierarchical Graph Alignment Kernels）解决了图卷积核函数在分解图形成非同构子结构并进行比较时忽视隐含相似性和拓扑位置信息所限制性能的问题，理论分析保证了该方法在复制核希尔伯特空间中为半正定且具有线性可分性，在各种基准数据集上与最先进的图卷积核函数进行比较证明了DHGAK的有效性和高效性。

深度分层图对齐核