## 4 Methodology
### Neighborhood Information Aggregate
#### 4.3.1 Aggregate Layer  
Early approaches to graph convolution sought to port two-dimensional convolutional networks onto irregular graphs [11], which naturally applied convolutions like in the image domain by representing solid networks onto planar matrices via time-frequency transformations; this category of approach is centered on acquiring knowledge regarding the structural characteristics of the network. Starting from GAT, the computation of node weights began to transition from being primarily based on the structural attributes of the network to being primarily reliant on the feature representations of individual nodes, but these models need to load the node features of the whole network when processing, which causes a certain training threshold and hinders the application of the models on large-scale networks.  
[PERSON] et al. proposed Graph Sample and Aggregated Embeddings (GraphSAGE) [46]. Unlike previous models that consider all neighboring nodes, Graph Sampling Aggregation Networks perform a random sampling of neighboring nodes such that each node's neighboring nodes are less than a given number of samples. However, GraphSAGE may introduce sample bias when nodes' neighbors have different degrees. For example, in a highly degree-centered graph, nodes with higher degrees may be selected more frequently in the sampling while nodes with lower degrees are ignored, causing the model to favor highly connected nodes in the node representation. Therefore, we considered the full sampling of neighboring nodes of a specific order and subsequently assigned the weights of the neighbor information of each order, which can avoid sampling bias without causing a dramatic increase in computational cost. In our designed aggregation layer, its job is to perform the multi-neighbor information aggregation of nodes; through the successive stacking of multiple aggregation layers, this process continually extends the aggregation from lower-order neighbors to higher-order neighbors, in addition to the information propagation between layers. Unlike GraphSAGE's gradually expanding sampling graph, we adopted the strategy of aggregating only the specified order of neighbor information at a time, i.e., when aggregating \(l\)-order neighbor information, we did not repeat the aggregation of \(l-1\)-order neighbor information (since the \(l-1\)-order neighbor information has already been accessed in the previous layer). In addition, each layer introduces a skip connection that skips directly to the last layer to correct the weights of the final aggregation result. The primary objective is to alleviate potential overfitting resulting from the increase in the number of convolutional layers and to diminish the influence of extraneous information. We define the form of the node update, as in (7):  
\[s^{(l+1)}=s^{(l)}+\frac{\sum_{i\in|N_{(l)}|}s_{i}^{(l)}}{|N_{(l)}|}. \tag{7}\]  
In the provided expression, \(s\) represents the node embedding of the current layer, \(l\) corresponds to the current layer number, and \(N_{(l)}\) signifies the set of nodes that are  
Figure 2: Hierarchical aggregation of neighbor nodes. Multiorder neighbors of a node are hierarchically aggregated for information and then attentively connected to obtain the target node representation.  
neighbors to node \"\(n\)\" at the \(l\)th order. Furthermore, \(|N_{(l)}|\) quantifies the total count of \(l\)th order neighbor nodes.