TY - JOUR
T1 - Graph Fourier transform based on singular value decomposition of the directed Laplacian
AU - Chen, Yang
AU - Cheng, Cheng
AU - Sun, Qiyu
PY - 2023/12
Y1 - 2023/12
N2 - 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. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
AB - 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. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
KW - Directed graphs
KW - Graph Fourier transform
KW - Graph signal processing
KW - Singular value decomposition
UR - http://www.scopus.com/inward/record.url?scp=85167463044&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85167463044&origin=recordpage
U2 - 10.1007/s43670-023-00062-w
DO - 10.1007/s43670-023-00062-w
M3 - RGC 21 - Publication in refereed journal
SN - 2730-5716
VL - 21
JO - Sampling Theory, Signal Processing, and Data Analysis
JF - Sampling Theory, Signal Processing, and Data Analysis
IS - 2
M1 - 24
ER -