Matrix Completion of Adaptive Jumping Graph Neural Networks for Recommendation Systems

Using graph neural networks to model recommendation scenarios can effectively capture high-order relationship features between objects, thereby helping the model better handle recommendation problems. However, the over-smoothing phenomenon poses a performance constraint for recommendation algorithms based on graph convolutional node aggregation. In realistic recommendation scenarios that involve social relationships, the imbalance of node degrees can deepen the impact of over-smoothing on recommendation accuracy. To address these issues, we propose an adaptive matrix completion algorithm for collaborative filtering recommendation, which is based on the aggregation rules of relational graph convolutional networks, and introduces jumping knowledge connection for adaptive selection of user-item feature aggregation results of deep graph convolutional networks. And in order to overcome the limitations of existing interlayer aggregation mechanisms, we design a self-attention-based aggregation mechanism to integrate the output of each layer and enhance the generalization ability of the model. In addition, we introduce normalization in the process of data transmission between layers to ensure the distinguishability between nodes. Finally, we conduct experiments on three real recommendation datasets to compare the algorithm's performance and perform ablation analysis. Our model achieves RMSEs of 0.9058, 0.8346 and 0.7176 on the three datasets respectively. The results show that the recommendation performance of our model achieves a leading level when compared with current state-of-the-art algorithms and verifies the influence of node degree distribution on the recommendation process.