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Title: Graph signal processing over a probability space of shift operators
Authors: Ji, Feng
Tay, Wee Peng
Ortega, Antonio
Keywords: Engineering::Electrical and electronic engineering
Issue Date: 2023
Source: Ji, F., Tay, W. P. & Ortega, A. (2023). Graph signal processing over a probability space of shift operators. IEEE Transactions On Signal Processing, 71, 1159-1174.
Project: MOE-T2EP20220-0002 
Journal: IEEE Transactions on Signal Processing 
Abstract: Graph signal processing (GSP) uses a shift operator to define a Fourier basis for the set of graph signals. The shift operator is often chosen to capture the graph topology. However, in many applications, the graph topology may be unknown a priori, its structure uncertain, or generated randomly from a predefined set for each observation. Each graph topology gives rise to a different shift operator. In this paper, we develop a GSP framework over a probability space of shift operators. We develop the corresponding notions of Fourier transform, MFC filters, and band-pass filters, which subsumes classical GSP theory as the special case where the probability space consists of a single shift operator. We show that an MFC filter under this framework is the expectation of random convolution filters in classical GSP, while the notion of bandlimitedness requires additional wiggle room from being simply a fixed point of a band-pass filter. We develop a mechanism that facilitates mapping from one space of shift operators to another, which allows our framework to be applied to a rich set of scenarios. We demonstrate how the theory can be applied by using both synthetic and real datasets.
ISSN: 1053-587X
DOI: 10.1109/TSP.2023.3263675
Schools: School of Electrical and Electronic Engineering 
Rights: © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at:
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:EEE Journal Articles

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