Discrete Signal Processing on Graphs

TLDR

In social settings, individuals form complex networks where each node generates data, producing signals indexed by graph nodes that differ from conventional time or image signals. The paper aims to extend discrete signal processing to graph‑indexed signals and demonstrate its utility by classifying blogs, compressing weather‑station data, and predicting mobile‑service customer behavior. The authors index data by graph nodes and extend DSP concepts—filters, convolution, z‑transform, impulse response, spectral representation, Fourier transform, and frequency response—to graph‑indexed signals.

Abstract

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.