Stationary Signal Processing on Graphs
TLDR
This paper generalizes the traditional concept of wide sense stationarity to signals defined over the vertices of arbitrary weighted undirected graphs and shows that stationarity is expressed through the graph localization operator reminiscent of translation.Abstract:
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.read more
Citations
More filters
Journal ArticleDOI
Graph Signal Processing: Overview, Challenges, and Applications
TL;DR: An overview of core ideas in GSP and their connection to conventional digital signal processing are provided, along with a brief historical perspective to highlight how concepts recently developed build on top of prior research in other areas.
Posted Content
Graph Signal Processing: Overview, Challenges and Applications
TL;DR: Graph Signal Processing (GSP) as discussed by the authors aims to develop tools for processing data defined on irregular graph domains, including sampling, filtering, and graph learning, which can be used for processing sensor network data, biological data, and image processing and machine learning.
Journal ArticleDOI
Connecting the Dots: Identifying Network Structure via Graph Signal Processing
TL;DR: Graph signal processing (GSP) has been widely used to infer the underlying graph topology as discussed by the authors, where correlation analysis takes center stage along with its connections to covariance selection and high dimensional regression for learning Gaussian graphical models.
Journal ArticleDOI
Network Topology Inference from Spectral Templates
TL;DR: The novel idea is to find a graph shift that, while being consistent with the provided spectral information, endows the network with certain desired properties such as sparsity, and develops efficient inference algorithms stemming from provably tight convex relaxations of natural nonconvex criteria.
Journal ArticleDOI
Stationary Graph Processes and Spectral Estimation
TL;DR: This paper proposes a definition of weak stationarity for random graph signals that takes into account the structure of the graph where the random process takes place, while inheriting many of the meaningful properties of the classical time domain definition.
References
More filters
Journal ArticleDOI
Fundamentals of statistical signal processing: estimation theory
TL;DR: The Fundamentals of Statistical Signal Processing: Estimation Theory as mentioned in this paper is a seminal work in the field of statistical signal processing, and it has been used extensively in many applications.
Book
Probability, random variables, and stochastic processes
TL;DR: In this paper, the meaning of probability and random variables are discussed, as well as the axioms of probability, and the concept of a random variable and repeated trials are discussed.
Journal ArticleDOI
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Amir Beck,Marc Teboulle +1 more
TL;DR: A new fast iterative shrinkage-thresholding algorithm (FISTA) which preserves the computational simplicity of ISTA but with a global rate of convergence which is proven to be significantly better, both theoretically and practically.
Journal ArticleDOI
The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms
TL;DR: In this article, the use of the fast Fourier transform in power spectrum analysis is described, and the method involves sectioning the record and averaging modified periodograms of the sections.
Book
Spectral Graph Theory
TL;DR: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigen values and quasi-randomness