Hierarchical Multi-Marginal Optimal Transport for Network Alignment
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909101242449920 |
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| author | Zeng, Zhichen Du, Boxin Zhang, Si Xia, Yinglong Liu, Zhining Tong, Hanghang |
| author_facet | Zeng, Zhichen Du, Boxin Zhang, Si Xia, Yinglong Liu, Zhining Tong, Hanghang |
| contents | Finding node correspondence across networks, namely multi-network alignment, is an essential prerequisite for joint learning on multiple networks. Despite great success in aligning networks in pairs, the literature on multi-network alignment is sparse due to the exponentially growing solution space and lack of high-order discrepancy measures. To fill this gap, we propose a hierarchical multi-marginal optimal transport framework named HOT for multi-network alignment. To handle the large solution space, multiple networks are decomposed into smaller aligned clusters via the fused Gromov-Wasserstein (FGW) barycenter. To depict high-order relationships across multiple networks, the FGW distance is generalized to the multi-marginal setting, based on which networks can be aligned jointly. A fast proximal point method is further developed with guaranteed convergence to a local optimum. Extensive experiments and analysis show that our proposed HOT achieves significant improvements over the state-of-the-art in both effectiveness and scalability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_04470 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hierarchical Multi-Marginal Optimal Transport for Network Alignment Zeng, Zhichen Du, Boxin Zhang, Si Xia, Yinglong Liu, Zhining Tong, Hanghang Machine Learning Artificial Intelligence Finding node correspondence across networks, namely multi-network alignment, is an essential prerequisite for joint learning on multiple networks. Despite great success in aligning networks in pairs, the literature on multi-network alignment is sparse due to the exponentially growing solution space and lack of high-order discrepancy measures. To fill this gap, we propose a hierarchical multi-marginal optimal transport framework named HOT for multi-network alignment. To handle the large solution space, multiple networks are decomposed into smaller aligned clusters via the fused Gromov-Wasserstein (FGW) barycenter. To depict high-order relationships across multiple networks, the FGW distance is generalized to the multi-marginal setting, based on which networks can be aligned jointly. A fast proximal point method is further developed with guaranteed convergence to a local optimum. Extensive experiments and analysis show that our proposed HOT achieves significant improvements over the state-of-the-art in both effectiveness and scalability. |
| title | Hierarchical Multi-Marginal Optimal Transport for Network Alignment |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2310.04470 |