Graph convolutional networks (GCNs) can successfully learn the graph signal representation by graph convolution. The graph convolution depends on the graph filter, which contains the topological dependency of data and propagates data features. However, the estimation errors in the propagation matrix (e.g., the adjacency matrix) can have a significant impact on graph filters and GCNs. In this paper, we study the effect of a probabilistic graph error model on the performance of the GCNs. We prove that the adjacency matrix under the error model is bounded by a function of graph size and error probability. We further analytically specify the upper bound of a normalized adjacency matrix with self-loop added. Finally, we illustrate the error bounds by running experiments on a synthetic dataset and study the sensitivity of a simple GCN under this probabilistic error model on accuracy.

翻译：图卷积网络（GCNs）能通过图卷积成功学习图信号表示。图卷积依赖于包含数据拓扑依赖关系并传播数据特征的图滤波器。然而，传播矩阵（如邻接矩阵）中的估计误差会对图滤波器及GCNs产生显著影响。本文研究了概率图误差模型对GCNs性能的影响。我们证明了在该误差模型下，邻接矩阵受限于图规模与误差概率的函数。进一步，我们从理论上给出了添加自环后的归一化邻接矩阵的上界。最后，通过在合成数据集上开展实验验证了误差界，并分析了简单GCN在该概率误差模型下对分类精度的灵敏度。