Due to their success at node classification, Graph Convolutional Networks (GCN) have raised a research upsurge of deep learning on graph-structured data. For the semi-supervised classification, graph convolution essentially acts as a low-pass filter on graph spectral domain. According to Graph Signal Processing theory, the low-pass filter in GCN is a finite impulse response (FIR) graph filter. However, compared with FIR graph filters, infinite impulse response (IIR) graph filters exhibit more powerful representation ability and flexibility. Intuitively, it is feasible to replace FIR filter in GCN with IIR graph filter to improve GCN. Therefore, inspired by the direct implementation of IIR graph filters, we propose a Bi-filtering Graph Convolutional Network (BGCN) which can be realized by simply cascading two sub filtering modules. Experimental results demonstrate that BGCN works well in node classification task and achieves comparable performance to GCN and its variants. The improvement of BGCN, however, is at the expense of a time-complexity increase. To simplify the proposed BGCN, we construct a Simple Bi-filtering Graph Convolution framework (SBGC) from the perspective of Graph Signal Processing. Furthermore, for the implementations of BGCN and SBGC, we design a novel low-pass graph filter to capture the low-frequency components that are beneficial to data representation for the task of node classification. Extensive experiments show that SBGC not only outperforms other baseline methods in performance, but also keeps a high level in computational efficiency. Moreover, it is particularly worth noting that both BGCN and SBGC are robust to feature noise and exhibit high label efficiency.

由于其在节点分类方面的成功，图卷积网络（GCN）引发了对图结构数据进行深度学习的研究热潮。对于半监督分类，图卷积本质上充当图谱域上的低通滤波器。根据图信号处理理论，GCN中的低通滤波器是有限脉冲响应（FIR）图滤波器。但是，与FIR图形滤波器相比，无限冲激响应（IIR）图形滤波器表现出更强大的表示能力和灵活性。从直觉上讲，用IIR图形滤波器替换GCN中的FIR滤波器以改善GCN是可行的。因此，受IIR图形滤波器直接实现的启发，我们提出了一种双滤波图形卷积网络（BGCN），可以通过简单地级联两个子滤波模块来实现。实验结果表明，BGCN在节点分类任务中表现良好，并且与GCN及其变体具有可比的性能。但是，BGCN的改进是以增加时间复杂性为代价的。为了简化提出的BGCN，我们从图信号处理的角度构造了一个简单的双滤波图卷积框架（SBGC）。此外，对于BGCN和SBGC的实现，我们设计了一种新颖的低通图滤波器，以捕获有益于节点分类任务数据表示的低频分量。大量的实验表明，SBGC不仅在性能上优于其他基准方法，而且还保持了较高的计算效率。而且，