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

arXiv: https://arxiv.org/abs/1908.01596 · HTML: https://mlsanity.com/paper/1908.01596/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2019.

## Built on by (most cited first, 5 of 5)

- [Graph Tensor Networks: An Intuitive Framework for Designing Large-Scale Neural Learning Systems on Multiple Domains](https://mlsanity.com/paper/2303.13565/) (2023)
- [Cluster-CAM: Cluster-Weighted Visual Interpretation of CNNs' Decision in Image Classification](https://mlsanity.com/paper/2302.01642/) (2023)
- [Online Graph Topology Learning via Time-Vertex Adaptive Filters: From Theory to Cardiac Fibrillation](https://mlsanity.com/paper/2411.01567/) (2024)
- [Locally Stationary Graph Processes](https://mlsanity.com/paper/2309.01657/) (2023)
- [Network Denoising Revisited: A Ricci-Flow-Inspired Graph Diffusion Method](https://mlsanity.com/paper/2608.16923/) (2026)

## Abstract (arXiv)

A class of doubly stochastic graph shift operators (GSO) is proposed, which is shown to exhibit: (i) lower and upper L2-boundedness for locally stationary random graph signals; (ii) L2-isometry for textiti.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.