Consensus Based Distributed Spectral Radius Estimation

A consensus based distributed algorithm to compute the spectral radius of a network is proposed. The spectral radius of the graph is the largest eigenvalue of the adjacency matrix, and is a useful characterization of the network graph. Conventionally, centralized methods are used to compute the spec...

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Bibliographic Details
Published in:IEEE signal processing letters Vol. 27; pp. 1045 - 1049
Main Authors: Muniraju, Gowtham, Tepedelenlioglu, Cihan, Spanias, Andreas
Format: Journal Article
Language:English
Published: New York IEEE 2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algebraic connectivity
Algorithms
Computer simulation
consensus
Convergence
Distributed algorithms
distributed estimation
Eigenvalues
Eigenvalues and eigenfunctions
Eigenvectors
Estimation
Graphs
Packet loss
Signal processing algorithms
Spectra
spectral radius
ISSN:1070-9908, 1558-2361
Online Access:Get full text
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Summary:A consensus based distributed algorithm to compute the spectral radius of a network is proposed. The spectral radius of the graph is the largest eigenvalue of the adjacency matrix, and is a useful characterization of the network graph. Conventionally, centralized methods are used to compute the spectral radius, which involves eigenvalue decomposition of the adjacency matrix of the underlying graph. Our distributed algorithm uses a simple update rule to reach consensus on the spectral radius, using only local communications. We consider time-varying graphs to model packet loss and imperfect transmissions, and provide the convergence characteristics of our algorithm, for both static and time-varying graphs. We prove that the convergence error is a function of principal eigenvector of adjacency matrix of the graph and reduces as <inline-formula><tex-math notation="LaTeX">\mathcal {O}(1/t)</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">t</tex-math></inline-formula> is the number of iterations. The algorithm works for any connected graph structure. Simulation results supporting the theory are also presented.
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ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2020.3003237