Graph Neural Network Model—Basic Idea and Process of PATCHY-SAN

1 Problems faced when applying CNN to graph-structured data:

1. Different receptive fields:
   When dealing with image problems, the convolutional neural network uses a fixed-size Kernel to extract image features, as shown in the figure below.
   
   When facing graph-structured data, since the number of first-order neighbors of each node in the network is different, if still It is not feasible to use a fixed-size kernel, because the receptive field of the convolution kernel will be different. Then when extracting the neighborhood, can the neighborhood be cut or padding to make the convolution operation feasible (Note: Not all nodes in the network are used as the central node to perform the convolutional neural network operation, but according to a function Sort the nodes first, and then select the top $w$ nodes as the central node).

2. When applying CNN to graph-structured data, the nodes of the graph lack order. Use a function (such as degree centrality, betweenness centrality, etc.) to sort the nodes.

3. How to learn node representations with a low computational complexity

2 PATCHY-SAN process

• General process:
  

1. Select node sequence:
   use function $l$ First sort all the nodes in the network, and then select the front$W$ nodes are used as central nodes.
   

2. Generate a neighborhood network for all nodes in the node sequence:
   Get the neighborhood network of each central node based on the breadth-first principle.

3. Normalize all obtained neighborhood networks.
   For neighborhood networks with too many or too few neighbor nodes, padding or pruning is performed according to the ordering of neighbor nodes. When selecting neighbor nodes, the distance between the vectors after mapping should be close to the distance of nodes in the network, that is, the following formula should be minimized
   

4. Using CNN to learn node representation

[1]: Niepert M, Ahmed M, Kutzkov K. Learning Convolutional Neural Networks for Graphs.
[2]: https://blog.csdn.net/zsfcg/article/details/82465973
[3]: https://www.cnblogs.com/KongHuZi/p/12720145.html