Writing
Graph Embedding
Graph embedding ideas, GCN convolution and pooling, spectral vs spatial convolutions, and GAT.
Graph Embedding Idea
Use deep learning to map graph nodes (or edges) to vectors, then cluster or classify in vector space.
Graph Convolutional Network (GCN)
Origin
Karate club graph; colors show modular communities.
GCN (Thomas Kipf, 2017, Semi-supervised classification with graph convolutional networks) brings CNN ideas from images to graphs.
GCN Convolution
CNN: convolution, pooling, FC, softmax
CNN process
GCN flow:
GCN pipeline
Pooling
Vertex matching and graph coarsening—merge or drop edges.
Pooling 1
Fuse by node index
Pooling 2
Convolution
Transform node signals to spectral domain, matrix decomposition, transform back.
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Input:
GCN input Output: 
Formula 1 
Formula 2 
Target 
Paper diagram ### Two convolution types: Spectral—paper https://arxiv.org/pdf/1609.02907.pdf, code https://github.com/tkipf/gcn -
Spatial convolution—https://www.leiphone.com/news/201706/ppA1Hr0M0fLqm7OP.html
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Graph Attention Network (GAT) ICLR 2018—https://github.com/Diego999/pyGAT, https://arxiv.org/pdf/1710.10903.pdf
GAT flow -
Idea Many graphs, different node counts—node classification. GCN needs the full graph; GAT classifies from a node’s and neighbors’ features only.