Abstract: With the widespread application of complex network analysis in many fields, such as recommendation systems, social networks, disease transmission networks, and financial transaction networks, the analysis of dynamic graphs has become a key challenge in the study of graph neural networks. To address the issue of embedding distortion caused by single-space embeddings in dynamic graph neural networks for link prediction, an adaptive product space discrete dynamic graph link prediction model (APSDG) is proposed. This model aims to resolve embedding distortion and enhance the performance of discrete dynamic graph link prediction. By integrating Euclidean space, hyperbolic space, and spherical space, a product space is constructed as the embedding space to better fit the complex structure of dynamic graph data. To achieve adaptive adjustment of the product space, a reinforcement learning mechanism is designed to dynamically optimize the dimensional proportions and curvature parameters of each space. Experimental results demonstrate that APSDG outperforms baseline models using single-space embeddings across five real-world datasets. In tasks of dynamic link prediction and dynamic new link prediction, APSDG achieves average gains in AUC and AP metrics of 2.24% and 1.90%, 2.12% and 1.43%, respectively, APSDG effectively solves the embedding distortion problem of single space embedding methods, can better capture the hierarchical structure and regular structure of complex networks, and significantly improves the dynamic link prediction effect.

Key words: discrete dynamic graph, representation learning, link prediction, product space, geometric deep learning, reinforcement learning

摘要： 随着复杂网络分析在诸多领域的广泛应用，如推荐系统、社交网络、疾病传播网络和金融交易网络，动态图的分析成为图神经网络研究的一个关键挑战。针对动态图神经网络在链接预测时因单一空间嵌入导致的嵌入扭曲问题，提出了自适应积空间离散动态图链接预测模型（APSDG），拟解决嵌入扭曲问题，提高离散动态图链接预测性能。通过结合欧几里得空间、双曲空间和超球面空间，构建积空间作为嵌入空间，以更好地拟合动态图数据的复杂结构。为实现积空间的自适应调整，设计了一种强化学习机制，动态优化各空间的维度比例和曲率参数。实验结果表明，APSDG在五个真实世界数据集上优于使用单一空间的基准模型，在动态链接预测和动态新链接预测任务中，AUC和AP指标上的平均增益分别为2.24%和1.90%，2.12%和1.43%, APSDG有效解决了单一空间嵌入方法的嵌入扭曲问题，能够更好地捕捉复杂网络的层次结构和规则结构，显著提升了动态链接预测效果。

关键词: 离散动态图, 表示学习, 链接预测, 积空间, 几何深度学习, 强化学习