Discrete Signal Processing on Graphs

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.

Cited by in corpus (6)

• Dynamic stochastic blockmodels for time-evolving social networks
• Local-set-based Graph Signal Reconstruction
• Local Measurement and Reconstruction for Noisy Graph Signals
• Phase Transitions in Spectral Community Detection of Large Noisy Networks
• Diffusion and Superposition Distances for Signals Supported on Networks
• Asymptotic Justification of Bandlimited Interpolation of Graph signals for Semi-Supervised Learning