A class of doubly stochastic shift operators for random graph signals and their boundedness.

Autor: Scalzo B; Imperial College London, London SW7 2AZ, UK., Stanković L; University of Montenegro, Džordža Vašingtona bb, 81000 Podgorica, Montenegro., Daković M; University of Montenegro, Džordža Vašingtona bb, 81000 Podgorica, Montenegro., Constantinides AG; Imperial College London, London SW7 2AZ, UK., Mandic DP; Imperial College London, London SW7 2AZ, UK. Electronic address: d.mandic@imperial.ac.uk.
Jazyk: angličtina
Zdroj: Neural networks : the official journal of the International Neural Network Society [Neural Netw] 2023 Jan; Vol. 158, pp. 83-88. Date of Electronic Publication: 2022 Nov 13.
DOI: 10.1016/j.neunet.2022.10.035
Abstrakt: A class of doubly stochastic graph shift operators (GSO) is proposed, which is shown to exhibit: (i) lower and upper L 2 -boundedness for locally stationary random graph signals, (ii) L 2 -isometry for i.i.d. random graph signals with the asymptotic increase in the incoming neighbourhood size of vertices, and (iii) preservation of the mean of any graph signal - all prerequisites for reliable graph neural networks. These properties are obtained through a statistical consistency analysis of the proposed graph shift operator, and by exploiting the dual role of the doubly stochastic GSO as a Markov (diffusion) matrix and as an unbiased expectation operator. For generality, we consider directed graphs which exhibit asymmetric connectivity matrices. The proposed approach is validated through an example on the estimation of a vector field.
Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
(Copyright © 2022 Elsevier Ltd. All rights reserved.)
Databáze: MEDLINE
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