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arXiv · 1908.01596

A Class of Doubly Stochastic Shift Operators for Random Graph Signals and their Boundedness

Bruno Scalzo Dees·Ljubisa Stankovic·Milos Dakovic·Anthony G. Constantinides·Danilo P. Mandic
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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 \textit{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. These properties are obtained through a statistical consistency analysis of the graph shift, and by exploiting the dual role of the doubly stochastic GSO as a Markov (diffusion) matrix and as an unbiased expectation operator. Practical utility of the class of doubly stochastic GSOs is demonstrated in a real-world multi-sensor signal filtering setting.

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Bruno Scalzo Dees, Ljubisa Stankovic, Milos Dakovic, Anthony G. Constantinides, Danilo P. Mandic. 2019-08-05. A Class of Doubly Stochastic Shift Operators for Random Graph Signals and their Boundedness. https://arxiv.org/abs/1908.01596

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