Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Data Domains

TLDR

High‑dimensional data in social, energy, transportation, sensor, and neuronal networks naturally reside on the vertices of weighted graphs, and signal processing on graphs combines algebraic and spectral graph theory with computational harmonic analysis to analyze such signals. This tutorial outlines the main challenges of graph signal processing, describes how graph spectral domains—analogous to classical frequency domains—are defined, and emphasizes the need to incorporate irregular graph structures in signal processing. We review how fundamental operations such as filtering, translation, modulation, dilation, and downsampling are generalized to graphs, survey localized multiscale transforms for efficient information extraction, and discuss open issues and possible extensions.

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 analogues 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.