A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications
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arXiv
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| Format: | Preprint |
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2024
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| author | Han, Jiaqi Cen, Jiacheng Wu, Liming Li, Zongzhao Kong, Xiangzhe Jiao, Rui Yu, Ziyang Xu, Tingyang Wu, Fandi Wang, Zihe Xu, Hongteng Wei, Zhewei Zhao, Deli Liu, Yang Rong, Yu Huang, Wenbing |
| author_facet | Han, Jiaqi Cen, Jiacheng Wu, Liming Li, Zongzhao Kong, Xiangzhe Jiao, Rui Yu, Ziyang Xu, Tingyang Wu, Fandi Wang, Zihe Xu, Hongteng Wei, Zhewei Zhao, Deli Liu, Yang Rong, Yu Huang, Wenbing |
| contents | Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections, making them ineffectively processed by current Graph Neural Networks (GNNs). To address this issue, researchers proposed a variety of geometric GNNs equipped with invariant/equivariant properties to better characterize the geometry and topology of geometric graphs. Given the current progress in this field, it is imperative to conduct a comprehensive survey of data structures, models, and applications related to geometric GNNs. In this paper, based on the necessary but concise mathematical preliminaries, we formalize geometric graph as the data structure, on top of which we provide a unified view of existing models from the geometric message passing perspective. Additionally, we summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation. We also discuss the challenges and future potential directions of geometric GNNs at the end of this survey. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00485 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications Han, Jiaqi Cen, Jiacheng Wu, Liming Li, Zongzhao Kong, Xiangzhe Jiao, Rui Yu, Ziyang Xu, Tingyang Wu, Fandi Wang, Zihe Xu, Hongteng Wei, Zhewei Zhao, Deli Liu, Yang Rong, Yu Huang, Wenbing Machine Learning Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections, making them ineffectively processed by current Graph Neural Networks (GNNs). To address this issue, researchers proposed a variety of geometric GNNs equipped with invariant/equivariant properties to better characterize the geometry and topology of geometric graphs. Given the current progress in this field, it is imperative to conduct a comprehensive survey of data structures, models, and applications related to geometric GNNs. In this paper, based on the necessary but concise mathematical preliminaries, we formalize geometric graph as the data structure, on top of which we provide a unified view of existing models from the geometric message passing perspective. Additionally, we summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation. We also discuss the challenges and future potential directions of geometric GNNs at the end of this survey. |
| title | A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2403.00485 |