The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains

TLDR

High‑dimensional data in networks such as social, energy, transportation, sensor, and neuronal systems naturally reside on graph vertices, and signal processing on graphs merges algebraic and spectral graph theory with harmonic analysis to analyze such signals. This tutorial overview outlines the main challenges of graph signal processing, defines graph spectral domains analogous to classical frequency domains, and emphasizes the need to account for irregular graph structures. We review methods that generalize fundamental operations such as filtering, translation, modulation, dilation, and downsampling to the graph setting, and survey localized, multiscale transforms that efficiently extract information from high‑dimensional graph data. We conclude with a brief discussion of 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.