Graph Laplacian Matrix Learning from Smooth Time-Vertex Signal

作     者：Ran Li Junyi Wang Wenjun Xu Jiming Lin Hongbing Qiu Ran Li;Junyi Wang;Wenjun Xu;Jiming Lin;Hongbing Qiu

作者机构：School of Telecommunications EngineeringXidian UniversityXi’an 710071ShanxiChina Key Laboratory of Cognitive Radio and Information ProcessingMinistry of Education(Guilin University of Electronic Technology)Guilin 541004GuangxiChina School of Information and Communication EngineeringBeijing University of Posts and TelecommunicationsBeijing 100876China 

出 版 物：《China Communications》 (中国通信（英文版）)

年 卷 期：2021年第18卷第3期

页      面：187-204页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(Grant No.61966007) Key Laboratory of Cognitive Radio and Information Processing,Ministry of Education(No.CRKL180106,No.CRKL180201) Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing,Guilin University of Electronic Technology(No.GXKL06180107,No.GXKL06190117) Guangxi Colleges and Universities Key Laboratory of Satellite Navigation and Position Sensing 

主　　题：Cartesian product graph discrete secondorder difference operator Gaussian prior distribution graph Laplacian matrix learning spatiotemporal smoothness time-vertex signal 

摘      要：In this paper,we focus on inferring graph Laplacian matrix from the spatiotemporal signal which is defined as“time-vertex signal.To realize this,we first represent the signals on a joint graph which is the Cartesian product graph of the time-and *** assuming the signals follow a Gaussian prior distribution on the joint graph,a meaningful representation that promotes the smoothness property of the joint graph signal is ***,by decoupling the joint graph,the graph learning framework is formulated as a joint optimization problem which includes signal denoising,timeand vertex-graphs learning ***,two algorithms are proposed to solve the optimization problem,where the discrete second-order difference operator with reversed sign(DSODO)in the time domain is used as the time-graph Laplacian operator to recover the signal and infer a vertex-graph in the first algorithm,and the time-graph,as well as the vertex-graph,is estimated by the other *** on both synthetic and real-world datasets demonstrate that the proposed algorithms can effectively infer meaningful time-and vertex-graphs from noisy and incomplete data.