# Deep Hierarchical Graph Alignment Kernels

arXiv: https://arxiv.org/abs/2405.05545 · HTML: https://mlsanity.com/paper/2405.05545/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 9 May 2024.

## Builds on (most cited first, 14 of 14)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [GraKeL: A Graph Kernel Library in Python](https://mlsanity.com/paper/1806.02193/) (2018)
- [On Valid Optimal Assignment Kernels and Applications to Graph Classification](https://mlsanity.com/paper/1606.01141/) (2016)
- [RetGK: Graph Kernels based on Return Probabilities of Random Walks](https://mlsanity.com/paper/1809.02670/) (2018)
- [Graph Filtration Kernels](https://mlsanity.com/paper/2110.11862/) (2021)
- [Gradual Weisfeiler-Leman: Slow and Steady Wins the Race](https://mlsanity.com/paper/2209.09048/) (2022)
- [A Hierarchical Transitive-Aligned Graph Kernel for Un-attributed Graphs](https://mlsanity.com/paper/2002.04425/) (2020)
- [Tree++: Truncated Tree Based Graph Kernels](https://mlsanity.com/paper/2002.09846/) (2020)
- [Multi-scale Wasserstein Shortest-path Graph Kernels for Graph Classification](https://mlsanity.com/paper/2206.00979/) (2022)

## Abstract (arXiv)

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).