Graph learning from band-limited data by graph Fourier transform analysis

Shan, B; Ni, W; Yuan, X; Yang, D; Wang, X; Liu, RP

Graph learning from band-limited data by graph Fourier transform analysis

Shan, B Ni, W

Yuan, X

Yang, D Wang, X Liu, RP

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Publisher:: ELSEVIER
Publication Type:: Journal Article
Citation:: Signal Processing, 2023, 207
Issue Date:: 2023-06-01

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Field	Value	Language
dc.contributor.author	Shan, B
dc.contributor.author	Ni, W https://orcid.org/0000-0002-4933-594X
dc.contributor.author	Yuan, X https://orcid.org/0000-0002-9167-1613
dc.contributor.author	Yang, D
dc.contributor.author	Wang, X
dc.contributor.author	Liu, RP
dc.date.accessioned	2024-04-12T04:54:00Z
dc.date.available	2024-04-12T04:54:00Z
dc.date.issued	2023-06-01
dc.identifier.citation	Signal Processing, 2023, 207
dc.identifier.issn	0165-1684
dc.identifier.issn	1872-7557
dc.identifier.uri	http://hdl.handle.net/10453/177830
dc.description.abstract	A graph provides an effective means to represent the statistical dependence or similarity among signals observed at different vertices. A critical challenge is to excavate graphs underlying observed signals, because of non-convex problem structure and associated high computational requirements. This paper presents a new graph learning technique that is able to efficiently infer the graph structure underlying observed graph signals. The key idea is that we reveal the intrinsic relation between the frequency-domain representation of general band-limited graph signals, and the graph Fourier transform (GFT) basis. Accordingly, we derive a new closed-form analytic expression for the GFT basis, which depends deterministically on the observed signals (as opposed to being solved numerically and approximately in the literature). Given the GFT basis, the estimation of the graph Laplacian, more explicitly, its eigenvalues, is convex and efficiently solved using the alternating direction method of multipliers (ADMM). Simulations based on synthetic data and experiments based on public weather and brain signal datasets show that the new technique outperforms the state of the art in accuracy and efficiency.
dc.language	English
dc.publisher	ELSEVIER
dc.relation.ispartof	Signal Processing
dc.relation.isbasedon	10.1016/j.sigpro.2023.108950
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	08 Information and Computing Sciences, 09 Engineering, 10 Technology
dc.subject.classification	Networking & Telecommunications
dc.subject.classification	40 Engineering
dc.subject.classification	46 Information and computing sciences
dc.title	Graph learning from band-limited data by graph Fourier transform analysis
dc.type	Journal Article
utslib.citation.volume	207
utslib.for	08 Information and Computing Sciences
utslib.for	09 Engineering
utslib.for	10 Technology
pubs.organisational-group	University of Technology Sydney
pubs.organisational-group	University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	University of Technology Sydney/Strength - GBDTC - Global Big Data Technologies
pubs.organisational-group	University of Technology Sydney/Faculty of Engineering and Information Technology/School of Electrical and Data Engineering
pubs.organisational-group	University of Technology Sydney/Strength - CCSP - Centre for Cyber Security and Privacy
utslib.copyright.status	closed_access	*
dc.date.updated	2024-04-12T04:53:58Z
pubs.publication-status	Published
pubs.volume	207

Abstract:

A graph provides an effective means to represent the statistical dependence or similarity among signals observed at different vertices. A critical challenge is to excavate graphs underlying observed signals, because of non-convex problem structure and associated high computational requirements. This paper presents a new graph learning technique that is able to efficiently infer the graph structure underlying observed graph signals. The key idea is that we reveal the intrinsic relation between the frequency-domain representation of general band-limited graph signals, and the graph Fourier transform (GFT) basis. Accordingly, we derive a new closed-form analytic expression for the GFT basis, which depends deterministically on the observed signals (as opposed to being solved numerically and approximately in the literature). Given the GFT basis, the estimation of the graph Laplacian, more explicitly, its eigenvalues, is convex and efficiently solved using the alternating direction method of multipliers (ADMM). Simulations based on synthetic data and experiments based on public weather and brain signal datasets show that the new technique outperforms the state of the art in accuracy and efficiency.

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http://hdl.handle.net/10453/177830