## 5 Summary and Outlook  
This paper proposes an SSP-AA model for sparse subgraph prediction. Firstly, based on the subgraph-based method, this model effectively enhances the performance in link prediction tasks and addresses the problems of sampling and training difficulties faced by traditional methods on large-scale graph structure data. Secondly, by incorporating the adaptive attention mechanism and the jumping knowledge module into the SSP-AA model, the adaptive attention mechanism empowers the model with self-adjusting weights, allowing the model to more accurately reflect the importance of different nodes in the graph structure. It resolves the issue of lacking adaptive weight allocation when aggregating neighbor node features and automatically assigns weights according to the relationships between nodes, thus better capturing the information in the graph structure. Lastly, the model employs the jumping knowledge module, which flexibly combines the node feature representations across different network layers, better distinguishing different node feature representations, and effectively enhances the expressive ability of nodes in the model. It resolves the over-smoothing problem caused by the increase in the number of layers in traditional graph neural networks. Compared to other advanced models, SSP-AA achieves the best average prediction performance in seven datasets on AUC indicators, demonstrating the effectiveness of these two modules in handling large-scale graph structure data. Furthermore, the SSP-AA model plays an important role in various applications such as knowledge graph-based Q&A systems, search engines, and social networks. Particularly, it plays a crucial role in the research of robots in the field of artificial intelligence and the training of semantic network models and has a significant impact on some large-scale knowledge networks. In future research, we will continue to focus on the following directions:  
1. Explore the application of graph augmentation techniques to the subgraphs within the SSP-AA model to further enhance its learning capability;
2. Further study the methods based on subgraphs by considering the use of edge personalization in neighborhood subgraphs for sampling subgraphs with more target node-specific information;
3. Explore integrating other advanced attention mechanisms and graph neural network modules into the SSP-AA model to better cope with complex graph structure data and real-world application scenarios;
4. For different tasks and datasets, research methods to adaptively adjust the model structure and parameters to automatically discover the optimal graph neural network configuration;
5. Explore extending this method to various large-scale knowledge graphs, such as clinical medical research, industrial Internet, network anomaly detection, and other various networks.  
Conceptualization, Y.G.; Methodology, Y.G.; Software, Y.G.; Validation, A.L., X.Z., J.G. and J.L.; Formal analysis, A.L., X.Z., J.G. and J.L.; Investigation, W.L. and X.Z.; Resources, J.G.; Data curation, Y.G. and A.L.; Writing--original draft, Y.G.; Writing--review & editing, W.L. and A.L.; Visualization, X.Z.; Supervision, W.L.; Project administration, W.L.; Funding acquisition, W.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Ningxia Natural Science Foundation (No.2021 AAC03215), National Natural Science Foundation of China (No.62066038, 61962001), and Key Research Project of Northern University for Nationalities (No.2021 JCYJ12).  
Not applicable.