Abstract
The first step for any graph signal processing (GSP) procedure is to learn the graph signal representation, i.e., to capture the dependence structure of the data into an adjacency matrix. Indeed, the adjacency matrix is typically not known a priori and has to be learned. However, it is learned with errors. A little attention has been paid to modelling such errors in the adjacency matrix, and studying their effects on GSP methods. However, modelling errors in the adjacency matrix will enable both to study the graph error effects in GSP and to develop robust GSP algorithms. In this paper, we therefore introduce practically justifiable graph error models. We also study, both analytically when possible and numerically, the graph error effect on the performance of GSP methods in different types of problems such as filtering of graph signals and independent component analysis of graph signals (graph decorrelation).
Highlights
IntroductionIn the classical signal processing setup where the digital signals are represented in terms of time series or vectors of spatial measurements (for example, measurements by sensor arrays), it is assumed that each point of a discrete signal depends on the preceding or spatially close point of the signal
In the classical signal processing setup where the digital signals are represented in terms of time series or vectors of spatial measurements, it is assumed that each point of a discrete signal depends on the preceding or spatially close point of the signal
The latter is of interest because it has been reported in graph signal processing (GSP) literature that deleting one edge can have immensely larger effect than deleting another edge
Summary
In the classical signal processing setup where the digital signals are represented in terms of time series or vectors of spatial measurements (for example, measurements by sensor arrays), it is assumed that each point of a discrete signal depends on the preceding or spatially close point of the signal. Robust methods were built for GSP tasks such as signal recovery, label propagation and clustering, when the knowledge of edgewise probabilities of errors in the graph topology is available. The starting point for studying GSP performance under the condition of imperfect knowledge of graph signal adjacency matrix is the modelling of graph errors. The aim of this paper is to develop justifiable and generic enough models for adjacency matrix mismatches It studies the effects of the mismatched adjacency matrix on the performance of some more traditional GSP applications such as filtering of graph signals as well as independent component analysis (ICA) of graph signals, which is referred to as graph decorrelation (GraDe) in the context of separating signals based on graph structure only. A is diag(A), and the notation N(0, σ 2 ) stands for Gaussian zeromean distribution with variance σ 2
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
