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

TL;DR

This paper reviews the emerging field of signal processing on graphs, which extends classical data analysis techniques to irregular network domains, addressing challenges and proposing methods for processing signals on graph-structured data.

Contribution

It provides a comprehensive overview of graph spectral domains, fundamental operations, and multiscale transforms tailored for high-dimensional data on graphs, highlighting recent advances and open issues.

Findings

Introduction of spectral domain concepts for graphs

Generalization of filtering and transformation operations to graphs

Survey of multiscale transforms for graph signals

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.