Deep Hierarchical Graph Alignment Kernels

TL;DR

Deep Hierarchical Graph Alignment Kernels (DHGAK) improve graph comparison by hierarchically aligning substructures in a deep embedding space, capturing implicit similarities and topological information for better performance.

Contribution

This paper introduces DHGAK, a novel graph kernel that hierarchically aligns substructures in a deep embedding space, enhancing graph similarity measurement.

Findings

DHGAK outperforms state-of-the-art graph kernels on benchmark datasets.

DHGAK is theoretically guaranteed to be positive semi-definite.

DHGAK demonstrates both effectiveness and efficiency in graph comparison.

Abstract

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).