Graph Fourier transform based on singular value decomposition of the directed Laplacian

The Graph Fourier transform (GFT) is a fundamental tool in graph signal processing. In this paper, based on singular value decomposition of the Laplacian, we introduce a novel definition of GFT on directed graphs, and use the singular values of the Laplacian to carry the notion of graph frequencies....

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Bibliographic Details
Published inSampling theory, signal processing, and data analysis Vol. 21; no. 2
Main Authors Chen, Yang, Cheng, Cheng, Sun, Qiyu
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2023
Subjects
Abstract Harmonic Analysis
Machine Learning
Mathematics
Mathematics and Statistics
Original Article
Signal,Image and Speech Processing
Graph Fourier transform
94A15
Directed graphs
94C15
94A12
Graph signal processing
42C05
Singular value decomposition
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Summary:The Graph Fourier transform (GFT) is a fundamental tool in graph signal processing. In this paper, based on singular value decomposition of the Laplacian, we introduce a novel definition of GFT on directed graphs, and use the singular values of the Laplacian to carry the notion of graph frequencies. We show that the proposed GFT has its frequencies and frequency components evaluated by solving some constrained minimization problems with low computational cost, and it could represent graph signals with different modes of variation efficiently. Moreover, the proposed GFT is consistent with the conventional GFT in the undirected graph setting, and on directed circulant graphs, it is the classical discrete Fourier transform, up to some rotation, permutation and phase adjustment.
ISSN:2730-5716
2730-5724
DOI:10.1007/s43670-023-00062-w