Stationary Signal Processing on Graphs

Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over graphs or networks. In this paper, we generalize the traditio...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2017-07, Vol.65 (13), p.3462-3477
Main Authors: Perraudin, Nathanael, Vandergheynst, Pierre
Format: Article
Language:English
Subjects:
Apexes
Correlation
covariance estimation
Data models
Data processing
Fourier transforms
gaussian markov random fields
graph signal processing
Graphs
Kernel
Laplace equations
Machine learning
Power spectral density
Regression models
Signal processing
Spectral analysis
spectral graph theory
Stationarity
Wiener filter
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Summary:Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over graphs or networks. In this paper, we generalize the traditional concept of wide sense stationarity to signals defined over the vertices of arbitrary weighted undirected graphs. We show that stationarity is expressed through the graph localization operator reminiscent of translation. We prove that stationary graph signals are characterized by a well-defined power spectral density that can be efficiently estimated even for large graphs. We leverage this new concept to derive Wiener-type estimation procedures of noisy and partially observed signals and illustrate the performance of this new model for denoising and regression.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2017.2690388