Spatial Graph Convolutional Network

A Spatial Graph Convolutional Network is a Graph Convolutional Network that defines convolutions directly on a graph.

• AKA: Spatial-Temporal Graph Neural Network.
• Context:
  • It can range from being a CNN-based Spatial Graph Network to being a Propagation-based Spatial Graph Convolutional Network.
• Example(s):
  • Diffusion Convolutional Neural Network (Atwood & Towsley, 2016),
  • PATCHY-SAN (Niepert et al., 2016),
  • Message Passing Neural Network (Gilmer et al., 2017),
  • GraphSage (Hamilton et al., 2017),
  • Learnable Graph Convolutional Network (Gao et al., 2018),
  • ...
  • …
• Counter-Example(s):
  • a Spectral Graph Convolutional Network,
  • a Graph Attention Network (GAT),
  • a Graph Recurrent Network (GRN),
  • a Graph Wavelet Neural Network (GWNN).
• See: Recurrent Neural Network, Feedforward Neural Network, Attention Mechanism.

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References

2020a

• (Wu et al., 2020) ⇒ Zonghan Wu, Shirui Pan, Fengwen Chen, Guodong Long, Chengqi Zhang, and Philip S. Yu (2020). "A Comprehensive Survey on Graph Neural Networks". In: IEEE transactions on neural networks and learning systems, 32(1), 4-24.
  • QUOTE: In 2009, Micheli et al. first addressed graph mutual dependency by architecturally composite non-recursive layers while inheriting ideas of message passing from RecGNNs. However, the importance of this work was overlooked. Until recently, many spatial-based ConvGNNs (e.g., Stoudenmire & Schwab, 2001; Niepert et al., 2016; Gilmer et al., 2017) emerged.

2020b

• (Zhou et al., 2020) ⇒ Jie Zhou, Ganqu Cui, Shengding Hu, Zhengyan Zhang, Cheng Yang, Zhiyuan Liu, Lifeng Wang, Changcheng Li, and Maosong Sun (2020). "Graph neural networks: A review of methods and applications". AI Open, 1, 57-81.
  • QUOTE: Spatial approaches define convolutions directly on the graph based on the graph topology. The major challenge of spatial approaches is defining the convolution operation with differently sized neighborhoods and maintaining the local invariance of CNNs.

2019

• (Zhang et al., 2019) ⇒ Si Zhang, Hanghang Tong, Jiejun Xu, and Ross Maciejewski (2019). "Graph convolutional networks: a comprehensive review". In: Computational Social Networks, 6(1), 1-23.
  • QUOTE: In this section, we categorize the spatial graph convolutional networks into the classic CNN-based models, propagation-based models, and other related general frameworks.

2018

• (Gao et al., 2018) ⇒ Hongyang Gao, Zhengyang Wang, and Shuiwang Ji (2018). "Large-Scale Learnable Graph Convolutional Networks". In: Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (KDD 2018).

2017a

• (Gilmer et al., 2017) ⇒ Justin Gilmer, Samuel S. Schoenholz, Patrick F. Riley, Oriol Vinyals, and George E. Dahl (2017)."Neural Message Passing for Quantum Chemistry". In: Proceedings of the 34th International Conference on Machine Learning (PMLR 2017).

2017b

• (Hamilton et al., 2017) ⇒ William L. Hamilton, Rex Ying, and Jure Leskovec (2017). "Inductive Representation Learning on Large Graphs". In: Proceeding of the 31st Conference on Neural Information Processing Systems (NIPS 2017).

2016a

• (Atwood & Towsley, 2016) ⇒ James Atwood, and Don Towsley (2016). "Diffusion-Convolutional Neural Networks". In: Proceedings of Advances in Neural Information Processing Systems 29 (NIPS 2016).

2016b

• (Niepert et al., 2016) ⇒ Mathias Niepert, Mohamed Ahmed, and Konstantin Kutzkov (2016). "Learning Convolutional Neural Networks for Graphs" In: Proceedings of The 33rd International Conference on Machine Learning (PMLR 2016).

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