Discrete Signal Processing on Graphs

TL;DR

This paper extends discrete signal processing techniques to signals on graphs, enabling analysis and processing of data indexed by complex network nodes, with applications in social networks, weather data, and customer behavior prediction.

Contribution

It introduces a comprehensive framework for DSP on graphs, including filters, spectral analysis, and transforms, adapting classical DSP concepts to irregular graph-structured data.

Findings

Effective classification of blogs using graph-based DSP methods

Successful prediction and compression of weather station data

Behavior prediction of mobile service customers using graph 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.