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Geometric Deep Learning: Going beyond Euclidean data
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Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains, such as graphs and manifolds. The purpose of this article is to overview different examples of geometric deep-learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field.
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Shen, W. X., Liu, Y., Chen, Y., Zeng, X., Tan, Y., Jiang, Y. Y., & Chen, Y. (2022) · Nucleic Acids Research · doi:10.1093/nar/gkac010 · Cited by 34
A discriminative SPD feature learning approach on Riemannian manifolds for EEG classification
Kim, B. H., Choi, J. W., Lee, H., & Jo, S. (2023) · Pattern Recognition · doi:10.1016/j.patcog.2023.109751 · Cited by 36
Beyond Grid Data: Exploring graph neural networks for Earth observation
Zhao, S., Chen, Z., Xiong, Z., Shi, Y.-L., Saha, S., & Zhu, X. X. (2024) · IEEE Geoscience and Remote Sensing Magazine · doi:10.1109/mgrs.2024.3493972 · Cited by 48
Peivaste, I., Belouettar, S., Mercuri, F., Fantuzzi, N., Dehghani, H., Izadi, R., Ibrahim, H., Lengiewicz, J., Belouettar-Mathis, M., Bendine, K., et al. (2025) · Composite Structures · doi:10.1016/j.compstruct.2025.119419 · Cited by 51
Exploiting Relational Information in Social Networks using Geometric Deep Learning on Hypergraphs
Arya, D., & Worring, M. (2018) · International Conference on Multimedia Retrieval · doi:10.1145/3206025.3206062 · Cited by 35
Zhang, Q., Li, W., Li, H., & Wang, J. (2020) · Information Sciences · doi:10.1016/j.ins.2020.02.058 · Cited by 36
Representation Learning on Visual-Symbolic Graphs for Video Understanding
Mavroudi, E., Béjar, B., & Vidal, R. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-58526-6_5 · Cited by 36
GraphMDN: Leveraging graph structure and deep learning to solve inverse problems
Oikarinen, T., Hannah, D., & Kazerounian, S. (2021) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn52387.2021.9534301 · Cited by 37
Predicting waves in fluids with deep neural network
Deo, I. K., & Jaiman, R. K. (2022) · Physics of Fluids · doi:10.1063/5.0086926 · Cited by 36
Metadata
- Authors
- Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A., & Vandergheynst, P.
- Affiliations
- Tel Aviv University (IL)
- Courant Institute of Mathematical Sciences (US)
- Meta (United Kingdom) (GB)
- Meta (United States) (US)
- École Polytechnique Fédérale de Lausanne (CH)
- Venue
- IEEE Signal Processing Magazine
- Published
- 2017-07
- Volume
- 34
- Issue
- 4
- Pages
- 18-42
- ISSN
- 1053-5888 (ISSN-L)
- 1558-0792
- OpenAlex
- W2558748708
- Cited by
- 3,661
- References
- 137
- Citations by year
- 2026: 350 · 2025: 412 · 2024: 388 · 2023: 428 · 2022: 462 · 2021: 567 · 2020: 493 · 2019: 353 · 2018: 181 · 2017: 25
- FWCI
- 169.40
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Signal Processing Magazine (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Advanced Graph Neural Networks
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › 3D Shape Modeling and Analysis
- Keywords
- geometric deep learning, non-Euclidean data, graph neural networks, manifold learning, structured data, deep neural network
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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