A class of doubly stochastic shift operators for random graph signals and their boundedness. (January 2023)

• Record Type: Journal Article
• Authors: Scalzo, Bruno; Stanković, Ljubiša; Daković, Miloš; Constantinides, Anthony G.; Mandic, Danilo P.
• Is Part Of: Neural networks. Volume 158(2023)
• Page Start: 83
• Page End: 88
• Publication Date: 2023-01
• Subjects: Graph signal processing -- Doubly stochastic matrix -- Shift operator -- Statistical consistency -- Boundedness analysis -- Graph neural networks; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2022.10.035
• Languages: English
• ISSNs: 0893-6080

Abstract

Abstract: 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.