{"title":"基于SVD的有向积图的图傅立叶变换","authors":"Cheng Cheng;Yang Chen;Yeon Ju Lee;Qiyu Sun","doi":"10.1109/TSIPN.2023.3299511","DOIUrl":null,"url":null,"abstract":"Graph Fourier transform (GFT) is one of the fundamental tools in graph signal processing to decompose graph signals into different frequency components and to represent graph signals with strong correlation by different modes of variation in an effective way. The GFT on undirected graphs has been well studied and several approaches have been proposed to define GFTs on directed graphs. In this article, based on the singular value decompositions of some graph Laplacians, we propose two GFTs on the Cartesian product graph of two directed graphs. We show that the proposed GFTs could represent spatial-temporal data sets on directed graphs with strong correlation efficiently, and in the undirected graph setting they are essentially the joint GFT in the literature. In this article, we also consider the bandlimiting procedure in frequency domains of the proposed GFTs, and demonstrate their performances on denoising the hourly temperature data sets collected at 32 weather stations in the region of Brest (France) and at 218 locations in the United States.","PeriodicalId":56268,"journal":{"name":"IEEE Transactions on Signal and Information Processing over Networks","volume":"9 ","pages":"531-541"},"PeriodicalIF":3.0000,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/6884276/10040263/10195957.pdf","citationCount":"0","resultStr":"{\"title\":\"SVD-Based Graph Fourier Transforms on Directed Product Graphs\",\"authors\":\"Cheng Cheng;Yang Chen;Yeon Ju Lee;Qiyu Sun\",\"doi\":\"10.1109/TSIPN.2023.3299511\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Graph Fourier transform (GFT) is one of the fundamental tools in graph signal processing to decompose graph signals into different frequency components and to represent graph signals with strong correlation by different modes of variation in an effective way. The GFT on undirected graphs has been well studied and several approaches have been proposed to define GFTs on directed graphs. In this article, based on the singular value decompositions of some graph Laplacians, we propose two GFTs on the Cartesian product graph of two directed graphs. We show that the proposed GFTs could represent spatial-temporal data sets on directed graphs with strong correlation efficiently, and in the undirected graph setting they are essentially the joint GFT in the literature. In this article, we also consider the bandlimiting procedure in frequency domains of the proposed GFTs, and demonstrate their performances on denoising the hourly temperature data sets collected at 32 weather stations in the region of Brest (France) and at 218 locations in the United States.\",\"PeriodicalId\":56268,\"journal\":{\"name\":\"IEEE Transactions on Signal and Information Processing over Networks\",\"volume\":\"9 \",\"pages\":\"531-541\"},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2023-07-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://ieeexplore.ieee.org/iel7/6884276/10040263/10195957.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Transactions on Signal and Information Processing over Networks\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10195957/\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Signal and Information Processing over Networks","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10195957/","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
SVD-Based Graph Fourier Transforms on Directed Product Graphs
Graph Fourier transform (GFT) is one of the fundamental tools in graph signal processing to decompose graph signals into different frequency components and to represent graph signals with strong correlation by different modes of variation in an effective way. The GFT on undirected graphs has been well studied and several approaches have been proposed to define GFTs on directed graphs. In this article, based on the singular value decompositions of some graph Laplacians, we propose two GFTs on the Cartesian product graph of two directed graphs. We show that the proposed GFTs could represent spatial-temporal data sets on directed graphs with strong correlation efficiently, and in the undirected graph setting they are essentially the joint GFT in the literature. In this article, we also consider the bandlimiting procedure in frequency domains of the proposed GFTs, and demonstrate their performances on denoising the hourly temperature data sets collected at 32 weather stations in the region of Brest (France) and at 218 locations in the United States.
期刊介绍:
The IEEE Transactions on Signal and Information Processing over Networks publishes high-quality papers that extend the classical notions of processing of signals defined over vector spaces (e.g. time and space) to processing of signals and information (data) defined over networks, potentially dynamically varying. In signal processing over networks, the topology of the network may define structural relationships in the data, or may constrain processing of the data. Topics include distributed algorithms for filtering, detection, estimation, adaptation and learning, model selection, data fusion, and diffusion or evolution of information over such networks, and applications of distributed signal processing.