Discrete Signal Processing on Graphs
Open accessAbstract
In social settings, individuals interact through webs of relationships. Each individual is a node in a complex network (or graph) of interdependencies and generates data, lots of data. We label the data by its source, or formally stated, we index the data by the nodes of the graph. The resulting signals (data indexed by the nodes) are far removed from time or image signals indexed by well ordered time samples or pixels. DSP, discrete signal processing, provides a comprehensive, elegant, and efficient methodology to describe, represent, transform, analyze, process, or synthesize these well ordered time or image signals. This paper extends to signals on graphs DSP and its basic tenets, including filters, convolution,z-transform, impulse response, spectral representation, Fourier transform, frequency response, and illustrates DSP on graphs by classifying blogs, linear predicting and compressing data from irregularly located weather stations, or predicting behavior of customers of a mobile service provider.
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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 [83]
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Perraudin, N., Ricaud, B., Shuman, D. I., & Vandergheynst, P. (2018) · APSIPA Transactions on Signal and Information Processing · doi:10.1017/atsip.2018.2 · Cited by 58 · see citing works
Deep learning approaches for similarity computation: A survey
Yang, P., Wang, H., Yang, J., Qian, Z., Zhang, Y., & Lin, X. (2024) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2024.3422484 · Cited by 28 · see citing works
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- Authors
- Sandryhaila, A., & Moura, J. M. F.
- Affiliations
- Carnegie Mellon University (US)
- ORCID
- Moura, José M. F.
- Venue
- IEEE Transactions on Signal Processing
- Published
- 2013-04
- Volume
- 61
- Issue
- 7
- Pages
- 1644-1656
- ISSN
- 1053-587X (ISSN-L)
- 1941-0476
- OpenAlex
- W1991252559
- Cited by
- 1,531
- References
- 0
- Citations by year
- 2026: 90 · 2025: 102 · 2024: 115 · 2023: 109 · 2022: 123 · 2021: 153 · 2020: 171 · 2019: 153 · 2018: 157 · 2017: 150 · 2016: 99 · 2015: 69 · 2014: 28 · 2013: 12
- FWCI
- 76.69
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Transactions on Signal Processing (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- 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
- graph signal processing, discrete-time signal processing, graph filters, graph convolution, z-transform, impulse response, spectral representation, Fourier transform, frequency response, social networks, complex networks, linear prediction, weather station data, customer behavior prediction
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