从图卷积网络到图散射网络:回顾与展望  

From graph convolution networks to graph scattering networks:a survey

作　　者：柳世禹 戴文睿 李成林 熊红凯[1] Liu Shiyu;Dai Wenrui;Li Chenglin;Xiong Hongkai(School of Electronic Information and Electrical Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学电子信息与电气工程学院,上海200240

出　　处：《中国图象图形学报》2024年第1期45-64,共20页Journal of Image and Graphics

基　　金：国家自然科学基金项目(61932022)。

摘　　要：在图像与图形处理中,非欧氏空间数据与传统欧氏空间数据共同构成了数据的不同表达形式。随着面向图像、音频等传统信号的处理技术已经发展了数十年并趋于成熟,诸如图等非欧氏空间数据的兴起,对非欧氏空间的数据处理提取提出了更高的要求。图卷积网络的出现将面向传统信号的深度学习网络模型和卷积操作拓展到了图上,在一定程度上解决了学术界和工业界对图信号处理的需求。然而,空域特征聚合的图卷积网络容易产生过平滑问题。本文回顾了从图卷积网络到图散射网络的发展进程,分别梳理空域图卷积网络和谱域图卷积网络;并以图卷积网络为桥梁引出了图散射网络,比较和总结了图散射网络的前沿的理论和方法。传统的谱域图卷积网络虽然可以通过滤波器设计避免过平滑问题,但由于可训练参数较少、输出特征比较单一,往往存在表达能力不足的问题。图散射网络的提出很好地解决了图卷积网络中存在的问题。一方面,图散射变换将面向传统信号的散射变换操作拓展到图信号处理上,通过多尺度小波分解提取图信号的多分辨率特征,在保证网络稳定性的前提下解决了空域图卷积网络的特征过平滑问题;另一方面,相较于传统的谱域图卷积网络,图散射网络输出能够提取多尺度带通特征,增强模型的表达能力,提高了图分类等任务的结果。最后分析了现有图散射技术和理论的局限性,并提出了未来图散射网络可能的研究方向。In image processing and computer graphics,non-Euclidean data such as graphs have gained increasing attention in recent years because Euclidean data such as images and videos fail to represent data with structure information.Compared with traditional Euclidean data,the scale of a graph can be arbitrary large.The structure of a graph usually contains information such as the relation between vertices,the logical sequences,and the properties of graph itself.While images can be easily converted into graphs based on the Euclidean position of pixels,graphs(especially for irregular graphs)can merely be converted into images.Therefore,graphs require a higher level of representation learning compared with traditional Euclidean data.However,in the era of deep learning,traditional convolution neural networks(CNNs)fail to learn representations for graphs due to permutation covariance for nodewise features and permutation invariance for outputs such as classification labels.The performance of CNNs in graph representation learning is still limited even if inputs are augmented by arbitrary permutation during training to learn permutation covariance.The development of graph neural networks and graph convolution operations achieves milestone in representation learning of non-Euclidean data such as graphs.Commonly,graph convolution neural networks(GCNs)can be divided into two categories:spatial GCNs and spectral GCNs.Spatial GCNs focus on the establishment of neighborhood and update with aggregation functions that combine the features of the center vertex and its neighbors.Though GCNs based on neighborhood feature aggregation encourage the propagation of nodewise features,deep GCNs usually suffer from oversmoothness issue,and the features of vertices become indistinguishable.Therefore,later works consider introducing skip connections in deep GCNs or constructing shallow GCNs with multiscale neighborhood considered within each convolution to alleviate this issue.Spectral GCNs focus on the graph spectral theorem and update their para

关 键 词：深度学习 图卷积网络(GCN) 图散射网络(GSN) 表征学习 稳定性 信号扰动 拓扑扰动 

分 类 号：TP37[自动化与计算机技术—计算机系统结构]