基于盖根堡多项式最佳平方近似的谱图网络

Spectral graph networks based on best square approximation with Gegenbauer polynomials

针对现有谱图神经网络模型在学习图节点特征矩阵信号频率分布方面存在的不足,采用盖根堡正交基改进,提出一种泛化能力强、适合真实世界数据的谱图神经网络模型,有效提高节点分类任务精度。分析不同真实世界数据集中图节点特征矩阵的信号频率分布,使用盖根堡正交基学习谱图滤波函数,提高模型的泛化能力。理论分析表明,该模型能够以最佳平方误差有效学习闭区间上的任意连续谱滤波函数。在13个数据集上进行试验的结果显示,基于盖根堡正交基的谱图神经网络模型在8个数据集上的性能均超越目前的先进模型,验证了模型的有效性。可扩展性试验表明,该模型适用于大规模图数据。

To address the limitations of existing spectral graph neural network models in learning the frequency distribution of signals in graph node feature matrices,a Gegenbauer-based spectral graph neural network model with strong generalization ability was pro-posed,suitable for real-world data,which effectively improved node classification accuracy.The signal frequency distribution in graph node feature matrices from various real-world datasets was analyzed,and a method using the Gegenbauer orthogonal basis to learn spectral graph filtering functions was proposed,enhancing the model′s generalization ability.Theoretical analysis demonstrated that the model was capable of effectively learning arbitrary continuous spectral filtering functions on closed intervals with the best square error.Experiments conducted on 13 datasets showed that the performance of the Gegenbauer-based spectral graph neural net-work model surpassed advanced models on 8 out of 13 datasets,which confirmed the model′s effectiveness.Scalability experiments indicated that the model was applicable to large-scale graph data.