Discrete Signal Processing on Graphs

• Published in: IEEE transactions on signal processing Vol. 61; no. 7; pp. 1644 - 1656
• Main Authors: Sandryhaila, A., Moura, J. M. F.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2013; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Detection, estimation, filtering, equalization, prediction; Digital signal processing; Exact sciences and technology; Fourier transforms; Graph Fourier transform; Graphical models; Information, signal and communications theory; Laplace equations; Manifolds; Markov random fields; network science; Signal and communications theory; signal processing; Signal, noise; Telecommunications and information theory; Fourier transformation; Probabilistic approach; Wireless telecommunication; Mobile communication; Markov model; Markov random fields; Graph Fourier transform; Random field; Convolution; Pulse response; Z transformation; graphical models; Signal processing; Frequency response; Discrete signal; Digital signal processor; Blog; Telecommunication services; network science
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2013.2238935

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.