IEEE Signal Processing Magazine· 2013Q1
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains
- 4,454citations
- Q1SCImago
- 2013year
Short summary
Signal processing on graphs merges graph theory with harmonic analysis to process high-dimensional data residing on network structures. This field develops methods to adapt fundamental operations like filtering and downsampling to irregular graph domains.
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Key points
- High-dimensional data naturally resides on graph vertices in applications like social and neuronal networks.
- Signal processing on graphs adapts algebraic and spectral graph theory with harmonic analysis.
- Methods are developed to generalize operations like filtering, translation, and downsampling to graph structures.
- Localized, multiscale transforms are surveyed for efficient information extraction from graph data.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. IEEE Signal Processing Magazine, 2013 · DOI ↗
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Field: Statistical and Nonlinear Physics
Statistical and Nonlinear PhysicsPhysics and Astronomy