分析大数据:非规则结构与图信号

Understanding big data:irregular structure and graph signal

图信号处理(GraphSignalProcessing,GSP)使用和扩展信号处理的处理手段,以处理定义于不规则图结构上的数据。文中介绍图信号处理的研究背景及其研究意义,对图信号处理中图信号、图移位算子、图傅里叶变换以及图滤波器等几个重要的基本概念进行了阐释。目前图信号处理研究极其活跃,已经涵盖很多方面,文中着重对其中3个方向的研究进展进行了梳理与分析,包括图信号的采样与重建、图结构的学习以及图滤波器设计。最后,对图信号处理相关研究进行了展望,提出了若干值得进一步研究的问题。

The graph signal processing(GSP)is an important tool for processing data defined in irregular graph domains.Firstly,the background and the research significance of GSP are explained.Then,the basic definitions are introduced,including the concepts of graph signal,graph shift operator,graph Fourier trans­form,and graph filter.Finally,current research progress of GSP is analyzed,including graph signal sam­pling and reconstruction,graph structure learning,and graph filter design.Based on the current research status,the future of GSP is prospected and several issues worthy of further study are pointed out.