Adaptive Graph Convolution Network (AGCN)

An Adaptive Graph Convolution Network (AGCN) is a Spectral Graph Convolutional Network that learns residual graph Laplacian.

• Example(s):
  • Adaptive Boosting Algorithm for Graph Convolutional Network (AdaGCN),
  • …
• Counter-Example(s):
  • a Dual Graph Convolutional Network,
  • a Learnable 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, Spectral Network.

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References

2020

• (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: AGCN. All of these models use the original graph structure to denote relations between nodes. However, there may have implicit relations between different nodes. The Adaptive Graph Convolution Network (AGCN) is proposed to learn the underlying relations (Li et al., 2018a). AGCN learns a “residual” graph Laplacian and add it to the original Laplacian matrix. As a result, it is proven to be effective in several graph-structured datasets.

2018

• (Li et al., 2018) ⇒ Ruoyu Li, Sheng Wang, Feiyun Zhu, and Junzhou Huang (2018). "Adaptive Graph Convolutional Neural Networks". In: Proceedings of The Thirty-Second AAAI Conference on Artificial Intelligence (AAAI-18).
  • QUOTE: In the paper, we propose a novel spectral graph convolution network that feed on original data of diverse graph structures. e.g the organic molecules that consist of a different number of benzene rings. To allow that, instead of shared spectral kernel, we give each individual sample in batch a customized graph Laplacian that objectively describes its unique topology. A customized graph Laplacian will lead to a customized spectral filter that combines neighbor features according to its unique graph topology.

Figure 2: Convolution kernel comparison. Red point: centre of kernel. Orange points: coverage of kernel. (1) 3 × 3 kernel of classical CNN on 2-D grid; (2) graphconv/neural fingerprint, strictly localized kernel; (3) GCN, K-localized kernel merely on the shared graph; (4) AGCN, K-localized kernel on adaptive graph (individual graph + learned residual graph). Edges from learned residual graph Laplacian are dash lines. Color of edge indicates the weights in spectral kernels. Levels of value as color bar.

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