## 3 The Proposed SSP-AA Model
### Adaptive Attention Mechanism  
In link prediction tasks, the feature information of most target node pairs originates from the features of neighboring nodes. Effectively learning the neighborhood features of target nodes requires considering the different levels of structural importance and association among neighborhood nodes. Therefore, to learn these vital features, it is necessary to learn attention mechanisms [40] in multi-layer spaces to capture different aspects of latent features. Aggregating neighboring features that have important relevance in different layers through the attention mechanism can construct comprehensive and expressive neighbor features. Consequently, an adaptive attention mechanism is incorporated into the SSP-AA model. By employing this mechanism, the SSP-AA model can dynamically allocate weights among neighboring nodes, allowing for the effective aggregation of neighbor node information to generate target node representations. As a result, the SSP-AA model exhibits a strong capability to express features in prediction tasks. In this section, we first calculate the attention between neighboring nodes in the current layer. Then, the attention weights are normalized. Finally, the feature representation of the current layer is obtained through node aggregation. (1) Calculation of the attention mechanism  
The attention weights in traditional attention mechanisms are computed by applying a shared attention mechanism to the hidden representations between node pairs. For the representation of node \(i\), the feature of node \(j\) plays a crucial role. Every node in the graph is related to all other nodes. Therefore, the formula for calculating attention weights is as follows:  
\[e_{ij}^{l}=LeakyReLU(\alpha^{T}\big{[}W^{l}h_{i}^{l}\parallel W^{l}h_{j}^{l} \big{]}+b_{ij}). \tag{1}\]  
The term \(b_{ij}\) represents an additional learnable bias term, used to adjust attention weights based on the relationship between nodes \(i\) and \(j\). By introducing this additional bias term in the module, the model can more easily adapt the weights between neighboring \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbols** & **Definitions** \\ \hline \(G\) & Undirected Graph \\ \(V\) & Nodes in the Undirected Graph \\ \(E\) & Edges in the Undirected Graph \\ \(h\) & Node Features \\ \(H\) & A Set of Node Features \\ \(W\) & Weight Matrix \\ \(l\) & The \(l\)st Layer of the Model \\ \(a\) & Weight Vector \\ \(b\) & Adjusted Weight Bias Term \\ \(e_{ij}\) & The Original Attention Score Between Nodes \(i\) and \(j\) \\ \(\sigma\) & Non-linear Activation Function \\ \hline \hline \end{tabular}
\end{table} 
Table 1: SSP-AA symbol definitions. nodes in sparse subgraphs, thereby capturing the features of the graph structure more effectively. The Leaky Rectified Linear Unit (_LeakyReLU_) is a nonlinear activation function and a variant of the Rectified Linear Unit (_ReLU_) activation function. The _LeakyReLU_ allows for a small, nonzero output for negative inputs to solve the dying neuron problem, thus ensuring all neurons in the neural network remain active. This helps to enhance the learning capability and performance of the model. Based on the output of the graph attention layer, we can obtain the output features \(H^{l+1}\) from \(H^{l}\). Inspired by the dot product formula, the dot product is applied to the attention calculation of output features. When the dot product of two vectors is large, their angle in space is smaller, implying they have a similar direction and hence a higher similarity. This method allows for a more accurate aggregation of nodes with high similarity during the node aggregation process, thus enhancing the model's performance. Therefore, this paper proposes using the dot product to measure the similarity between two vectors.