基于Ollivier-Ricci曲率的图扩散节点分类算法  

Graph diffusion node classification algorithm based on Ollivier-Ricci curvature

作　　者：孙宁[1] 李胤萱 张帅 汤璇 魏宪 Sun Ning;Li Yinxuan;Zhang Shuai;Tang Xuan;Wei Xian(School of Software,Liaoning Technical University,Huludao Liaoning 125105,China;School of Software Engineering,East China Normal University,Shanghai 200241,China)

机构地区：[1]辽宁工程技术大学软件学院,辽宁葫芦岛125105 [2]华东师范大学软件工程学院,上海200241

出　　处：《计算机应用研究》2025年第1期165-170,共6页Application Research of Computers

基　　金：上海市2023年度“科技创新行动计划”自然科学基金面上项目(22DZ2229004)。

摘　　要：为解决图扩散方法在处理复杂边关系时精度降低的局限性,提出了一种基于曲率的图扩散神经网络。首先,引入Ollivier-Ricci曲率量化图的边曲率,提供关于图结构的几何度量;其次,运用曲率调整随机转移矩阵的权重,根据几何关系进行相应的权重修改;最后,将处理后的曲率矩阵与图扩散矩阵结合,更新权重系数进行模型训练。实验结果表明,与传统的图扩散方法相比,改良后的方法保持了有效地平滑图信号和减少高频噪声的优点,并在不同边和节点数量的数据集上将精度提高0.3~2.0百分点。该方法通过优化图扩散的消息聚合,能够更有效地利用图结构中的节点信息和边权重,从而提升节点分类任务中的模型性能,为未来基于图方法的研究提供了更可靠的方法与实验。To address the limitations of reduced accuracy in graph diffusion methods when handling complex edge relationships,this paper proposed a curvature-based graph diffusion neural network.The method introduced Ollivier-Ricci curvature to quantify edge curvature,providing a geometric measure of graph structure.The algorithm adjusted the weights of the random transition matrix using curvature,modifying them based on geometric relationships.It then combined the processed curvature matrix with the graph diffusion matrix to update the weight coefficients for model training.Experimental results show that the improved method maintains the advantages of smoothing graph signals effectively and reducing high-frequency noise.It increased accuracy by 0.3 to 2.0 percentage points on datasets with varying numbers of edges and nodes.The method optimized message aggregation in graph diffusion,utilizing node information and edge weights within the graph structure more effectively.This enhancement improves model performance in node classification tasks and provides a reliable method and experimental basis for future graph-based research.

关 键 词：图神经网络 图扩散 Ollivier-Ricci曲率 节点分类 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]