The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains
Open accessAbstract
In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process such signals on graphs. In this tutorial overview, we outline the main challenges of the area, discuss different ways to define graph spectral domains, which are the analogs to the classical frequency domain, and highlight the importance of incorporating the irregular structures of graph data domains when processing signals on graphs. We then review methods to generalize fundamental operations such as filtering, translation, modulation, dilation, and downsampling to the graph setting and survey the localized, multiscale transforms that have been proposed to efficiently extract information from high-dimensional data on graphs. We conclude with a brief discussion of open issues and possible extensions.
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Spectral-based methods assume graphs to be undirected.
“They assume graphs to be undirected.”
From A Comprehensive Survey on Graph Neural Networks (2021) · cites this paper as [82]
Spectral-based approaches define graph convolutions by introducing filters from the perspective of graph signal processing, where the graph convolutional operation is interpreted as removing noises from graph signals.
“Spectralbased approaches define graph convolutions by introducing filters from the perspective of graph signal processing [82] where the graph convolutional operation is interpreted as removing noises from graph signals.”
From A Comprehensive Survey on Graph Neural Networks (2021) · cites this paper as [82]
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- Authors
- Shuman, D. I., Narang, S. K., Frossard, P., Ortega, A., & Vandergheynst, P.
- Affiliations
- École Polytechnique Fédérale de Lausanne (CH)
- University of Southern California (US)
- Venue
- IEEE Signal Processing Magazine
- Published
- 2013-05
- Volume
- 30
- Issue
- 3
- Pages
- 83-98
- ISSN
- 1053-5888 (ISSN-L)
- OpenAlex
- W2101491865
- Cited by
- 4,421
- References
- 2
- Citations by year
- 2026: 293 · 2025: 369 · 2024: 393 · 2023: 442 · 2022: 425 · 2021: 542 · 2020: 479 · 2019: 412 · 2018: 342 · 2017: 266 · 2016: 214 · 2015: 148 · 2014: 71 · 2013: 24
- FWCI
- 168.48
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Signal Processing Magazine (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Advanced Graph Neural Networks
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Graph Theory and Algorithms
- Keywords
- spectral graph analysis, graph signal processing, graph filtering, multiscale transforms, irregular domains, weighted graphs
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