图卷积神经网络基础图结构影响研究

Study on the Influence of Basic Graph Structure in Graph Convolutional Network

为进一步提高基于图卷积神经网络的半监督图节点分类的准确率,本文研究了基础图结构对图卷积神经网络的影响.通过对数据集(Cora、Citeseer及Pubmed)的图结构进行可视化,发现数据集(Cora、Citeseer)的图结构均为非连通图.通过研究非连通图中图拉普拉斯矩阵的"0"特征值和特征向量的特性,提出了通过对图拉普拉斯矩阵的"0"特征值对应的特征向量进行相关运算处理,获取非连通图最大连通分量的方法.该方法有效获取了数据集(Cora、Citeseer)图结构的最大连通分量,去除了非连通小分量.在该最大连通分量上利用3种先进的图卷积神经网络模型(GCN、GAT和GMNN)进行了实验验证,结果表明分类准确率提升了1%-4%,为其它包含小连通分量噪声的数据集更有效地利用图卷积神经网络模型训练提供了参考.

In order to further improve accuracy of semi-supervised nodes classification based on graph convolutional network,this paper studies the influence of basic graph structure on graph convolutional network.By visualizing graph structures of three benchmark datasets(Cora,Citeseer and Pubmed),it is found that graph structures of two datasets(Cora and Citeseer) are all non-connected graphs.By studying the characteristics of zero eigenvalues and eigenvectors of graph Laplacian in nonconnected graphs,a method is proposed to obtain the Maximum Clique of nonconnected graphs by correlation operation of eigenvectors corresponding to the zero eigenvalue of graph Laplacian.The Maximum Clique of graph structures of two datasets(Cora,Citeseer) are obtained effectively,and non-connected small components are removed.Three advanced graph convolutional neural network models(GCN,GAT and GMNN)are used for experimental verification.Our results show that the classification accuracy is improved by 1%-4%,which provides a reference for other data sets containing small connected component noise to train the model of graph convolutional network more effectively.