陈旭, 张其, 王叔洋,等.基于几何交互的离散动态图链接预测模型[J].河南理工大学学报（自然科学版）,2025,44(5):52-61.

CHEN X, ZHANG Q, WANG S Y,et al.Geometric interaction-based discrete dynamic graph link prediction model[J].Journal of Henan Polytechnic University(Natural Science) ,2025,44(5):52-61.

基于几何交互的离散动态图链接预测模型

陈旭1, 张其1, 王叔洋2, 景永俊1

1.北方民族大学 计算机科学与工程学院，宁夏 银川  750000；2.北方民族大学 电气信息工程学院，宁夏 银川  750000

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。  目的 动态图链接预测任务中单一几何空间嵌入方法往往存在嵌入扭曲问题，难以有效捕捉复杂网络中的层次结构和规则结构。  方法 提出一种基于几何交互的离散动态图（geometric interaction-based discrete dynamic graph， GIDG）链接预测模型。首先在欧几里得空间和双曲空间中分别进行特征聚合，提取规则结构和层次结构的嵌入特征；其次通过交互融合两种几何特征，获得更具表达能力的节点嵌入；然后，设计历史信息融合模块，用以平衡长期信息和短期信息的融合，进一步提升时间序列的预测能力；最后，通过概率交互融合模块，计算欧几里得和双曲空间中的链接预测概率，并通过自适应加权融合，得到最终链接预测结果。  结果 实验结果表明，GIDG在5个数据集上的表现优于基于欧几里得空间和双曲空间的先进基准模型，其在动态链接预测和动态新链接预测任务中的AUC指标平均增益分别为1.46%和0.81%，AP指标的平均增益分别为1.27%和1.70%。特别是在大型数据集上，GIDG的表现显著优于现有的先进基准模型，尤其是在处理复杂的层次结构和幂律分布图时展现出较强的优势。  结论 GIDG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，显著提升动态链接预测效果。

关键词:离散动态图;表示学习;链接预测;双曲空间;几何深度学习

DOI:10.16186/j.cnki.1673-9787.2024070021

基金项目:中央高校基本科研业务费专项资金资助项目（2023ZRLG13）；宁夏回族自治区重点研发项目（2023BDE02017）

收稿日期:2024/07/04

修回日期:2024/09/30

出版日期:2025/07/23

Geometric interaction-based discrete dynamic graph link prediction model

Chen Xu1, Zhang Qi1, Wang Shuyang2, Jing Yongjun1

1.College of Computer Science and Engineering， North Minzu University， Yinchuan  750000， Ningxia， China；2.College of Electrical and Information Engineering， North Minzu University， Yinchuan  750000， Ningxia， China

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. Objectives The single geometric space embedding method in the dynamic graph link prediction task often has the problem of embedding distortion， which makes it difficult to effectively capture the hierarchical and regular structures in complex networks. Methods A geometric interaction-based discrete dynamic graph（GIDG） link prediction model was proposed. Firstly， feature aggregation was performed in Euclidean space and hyperbolic space respectively to extract the embedding features of regular structure and hierarchical structure. Secondly， the two geometric features were interactively fused to obtain more expressive node embedding. Then， a historical information fusion module was designed to balance the fusion of long-term information and short-term information， further improving the prediction ability of time series. Finally， the link prediction probabilities in Euclidean and hyperbolic spaces were calculated through the probability interaction fusion module， and the final link prediction results were obtained through adaptive weighted fusion. Results Experimental results showed that GIDG outperformed the advanced baseline models based on Euclidean space and hyperbolic space on five datasets. The average gains of AUC indicators in dynamic link prediction and dynamic new link prediction tasks were 1.46% and 0.81%， and the average gains of AP indicators were 1.27% and 1.70%， respectively. Especially on large datasets， GIDG significantly outperformed the existing advanced baseline models， especially when dealing with complex hierarchical structures and power-law distribution graphs. Conclusions GIDG effectively solved the embedding distortion problem of single space embedding methods， could 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;hyperbolic space;geometric deep learning