Graph Neural Network

GCN(Graph Convolutional Network)

• https://arxiv.org/pdf/1609.02907.pdf

http://tkipf.github.io/graph-convolutional-networks/

• 그래프: $\mathcal{G} = \left( \mathcal{V}, \mathcal{E} \right)$
• N 개 노드: $\mathcal{V} = \left\{ v_1, v_2, \cdots, v_N \right\}$
• 노드 피쳐: $X \in \mathbb{R}^{N \times F}$
• 엣지: $\left( \upsilon_i, \upsilon_j \right) \in \mathcal{E}$
• 인접(adjacency) 행렬
  • $A \in \left\{ 0, 1 \right\}^{N \times N}$ (연결되어 있으면 1, 아니면 0), 또는 가중치 행렬 $A \in \mathbb{R}^{N \times N}$
  • self-connection이 있는 undirected graph의 인접 행렬: $\widetilde{A} = A + I_N$
• 대각 차수(diagonal degree) 행렬
  • $D_{ii} = \sum_j{A_{ij}}$
  • $\widetilde{D}_{ii} = \sum_j{\widetilde{A}_{ij}}$
• 특징(feature) 행렬
  • $H^l \in \mathbb{R}^{N \times D}$, $H^0 = X$
  • $H^{l+1} = \sigma \left( \widetilde{D}^{-\frac{1}{2}} \widetilde{A} \widetilde{D}^{-\frac{1}{2}} H^l W^l \right)$

GAT(Graph Attention Network)

• https://arxiv.org/pdf/1710.10903.pdf

MPNN(Message Passing Neural Network)

• https://arxiv.org/pdf/1704.01212v2.pdf

GIN(Graph Isomorphism Network)

• https://arxiv.org/pdf/1810.00826.pdf

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https://jcheminf.biomedcentral.com/articles/10.1186/s13321-022-00634-3