## 3 Route Planning Scheme Based on Scatter-GNN
### Problem Definition
The operation of the link prediction process is described as the Algorithm 3:
```
Graph \(G=(V,E,W)\) Forward propagation: 1. Del forward/self,h,adj: 2.  calculate the attention coefficient e,adjacent nodes and obtain: 3. \(\overset{\rightarrow}{v}_{i}^{\prime}=\sigma(\{\sum\limits_{k=1}^{K}\sum \limits_{n\in N_{i}}^{K}\alpha_{in}^{k}W^{k}\overset{\rightarrow}{v}_{n})\) \(\overset{\rightarrow}{v}_{j}^{\prime}=\sigma(\{\sum\limits_{k=1}^{K}\sum \limits_{n\in N_{j}}^{K}\alpha_{in}^{k}W^{k}\overset{\rightarrow}{v}_{n})\) 4.  if self.contents is False 5.  output layer does not perform linear transformation Mosaic feature vector: 6. Del _prepare_attentional_mechanism_input(self, W-h): 7. For eigenvector, characteristic matrix in n do 8.  all_combinations_matrix=w-h... 9. return all_combinations_matrix.view Attention Networks: 10. Del Link prediction(epoch,loss,P) 11. For i = 1 to epoch do 12.  for edge = 1 to N do 13. Get node p and q by dividing edge: \(\overset{\rightarrow}{e_{ij}}\overset{\rightarrow}{v_{j}}\overset{ \rightarrow}{C}\overset{\rightarrow}{v_{j}^{\prime}}\) 15.  for k=1 layer to K layer do 16.  calculate loss = \(-\frac{1}{|\mathcal{P}\cup N|}\ \sum\limits_{(i_{j})\in|\mathcal{P}\cup N|}e_{ij}\log P _{ij=1}+\left(1-e_{ij}\right)\log P_{ij=0}\) and gradient 17.  update parameter w and b 18.  save model 19. Return P Prediction: 20. For n = 1, 2,... N do 21. Generate neighborhood node lists \(N_{1}\), \(N_{2}\),..., \(N_{K}\) for k = 1, 2,..., K do 23.  input \(\overset{\rightarrow}{v_{i}}\overset{\rightarrow}{C}\overset{ \rightarrow}{v_{k}^{\prime}}\) to model 24.  if p \(\geq\) 0.5.  g.add_edges_from(\(v_{n}\),\(v_{k}^{\prime}\)) 26.  g.delete_edges_from(\(v_{k}^{\prime}\),\(N_{k}\)) 27.  output \(G=(V,E)\)
```
**Algorithm 3**Link Prediction. After the model training is over, this paper adds all routes whose existence probability is not less than 0.5 obtained through link prediction to the original network to construct a new route network. ### Calculation of Existing Route Probability Based on Scatter-GNN

After completing the neighbors of the edge site to obtain a new line map, this paper uses the GNN classifier to calculate the probability of the existence of the two lines of



## 4 Experimental Verification

In this paper, the Scatter-GNN model is applied to the high-speed railway network and compared with other recently proposed baselines. The final results show the predicted probabilities of the Scatter-GNN model for various possible planned routes. ### Baseline Algorithm

In this paper, four baselines proposed in recent years are selected for comparison experiments with Scatter-GNN. * DeepWalk: DeepWalk [51] obtains the node sequence by random walk in the graph, then uses the Word2 vec algorithm to obtain the vector representation of the node, and finally uses the logistic regression classifier for prediction. The parameters of the logistic regression classifier are all consistent with the Scatter-GNN;
* Node2 vec: Node2 vec [52] is an improved algorithm for DeepWalk. It obtains the node sequence by performing a biased random walk in the graph, and then obtains the vector representation of the node through the Word2 vec algorithm. Similar to the DeepWalk algorithm, the vector representation of the obtained node is input into the logistic regression classifier for prediction, and the classifier parameters are consistent with the Scatter-GNN;
* GCN: GCN [7] uses the convolution kernel to extract the structural features of the graph, and then combines the node features to train on the whole graph;
* GAT: GAT [8] enhances the vector representation of the target node by assigning different weights to each neighbor, and it is one of the most advanced GNN models in graph representation learning so far. ### Parameter Setting

In order to facilitate comparative analysis, the dimension of the node vector generated by all algorithms in the experiment is set to 64, and other parameters follow the original setting values.