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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.05545 |
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| _version_ | 1866914789340479488 |
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| author | Tang, Shuhao Tian, Hao Cao, Xiaofeng Ye, Wei |
| author_facet | Tang, Shuhao Tian, Hao Cao, Xiaofeng Ye, Wei |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05545 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deep Hierarchical Graph Alignment Kernels Tang, Shuhao Tian, Hao Cao, Xiaofeng Ye, Wei Machine Learning 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). |
| title | Deep Hierarchical Graph Alignment Kernels |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2405.05545 |