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Asynchronous Nonlinear Updates on Graphs

Teke, Oguzhan and Vaidyanathan, P. P. (2018) Asynchronous Nonlinear Updates on Graphs. In: 52nd Asilomar Conference on Signals, Systems, and Computers. IEEE , Piscataway, NJ, pp. 998-1002. ISBN 978-1-5386-9218-9.

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The notion of graph shift, introduced recently in graph signal processing, extends many classical signal processing techniques to graphs. Its practical importance follows from its localization: a single graph shift requires nodes to communicate only with their neighbors. However, communications should happen simultaneously, which requires a synchronization over the graph. In order to overcome this restriction, recent studies consider a random asynchronous variant of the graph shift, which is also suitable for autonomous networks. A graph signal under this randomized scheme is shown to converge (under mild conditions) to an eigenvector of the eigenvalue 1 of the operator even if the operator has other eigenvalues with magnitudes larger than unity. If the eigenvalue 1 does not exist, the operator can be easily normalized in theory. However, in practice, the normalization requires one to know the (dominant) eigenvalues, which may not be possible to obtain in large autonomous networks. To eliminate this limitation, this study considers the use of a nonlinearity in the updates making the scheme similar in spirit to the Hopfield neural network model. Our simulation results show that a graph signal still approaches the eigenvector of the dominant eigenvalue although the convergence is not exact. Nevertheless, approximation is sufficient to accomplish certain tasks including autonomous clustering.

Item Type:Book Section
Related URLs:
URLURL TypeDescription
Teke, Oguzhan0000-0002-1131-5206
Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© 2018 IEEE. This work was supported in parts by the ONR grants N00014-17-1-2732 and N00014-18-1-2390, the NSF grant CCF-1712633, and the Electrical Engineering Carver Mead Research Seed Fund of the California Institute of Technology.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-17-1-2732
Office of Naval Research (ONR)N00014-18-1-2390
Carver Mead Seed FundUNSPECIFIED
Subject Keywords:Autonomous networks, nonlinear filters, randomized iterations, autonomous clustering
Record Number:CaltechAUTHORS:20190301-154838714
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Official Citation:O. Teke and P. P. Vaidyanathan, "Asynchronous Nonlinear Updates on Graphs," 2018 52nd Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, 2018, pp. 998-1002. doi: 10.1109/ACSSC.2018.8645351
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93405
Deposited By: Tony Diaz
Deposited On:01 Mar 2019 23:55
Last Modified:16 Nov 2021 16:57

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