Article (Scientific journals)
Extended Adjacency and Scale-dependent Graph Fourier Transform via Diffusion Distances
Elias, Vitor R.M.; Alves Martins, Wallace; Werner, Stefan
2020In IEEE Transactions on Signal and Information Processing over Networks
Peer reviewed
 

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Keywords :
diffusion distances; diffusion maps; extended adjacency; graph signal processing; scale-dependent graph Fourier transform
Abstract :
[en] This paper proposes the augmentation of the adjacency model of networks for graph signal processing. It is assumed that no information about the network is available, apart from the initial adjacency matrix. In the proposed model, additional edges are created according to a Markov relation imposed between nodes. This information is incorporated into the extended-adjacency matrix as a function of the diffusion distance between nodes. The diffusion distance measures similarities between nodes at a certain diffusion scale or time, and is a metric adopted from diffusion maps. Similarly, the proposed extended-adjacency matrix depends on the diffusion scale, which enables the definition of a scale-dependent graph Fourier transform. We conduct theoretical analyses of both the extended adjacency and the corresponding graph Fourier transform and show that different diffusion scales lead to different graph-frequency perspectives. At different scales, the transform discriminates shifted ranges of signal variations across the graph, revealing more information on the graph signal when compared to traditional approaches. The scale-dependent graph Fourier transform is applied for anomaly detection and is shown to outperform the conventional graph Fourier transform.
Disciplines :
Electrical & electronics engineering
Author, co-author :
Elias, Vitor R.M.
Alves Martins, Wallace ;  University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)
Werner, Stefan;  Norwegian University of Science and Technology (NTNU) > Department of Electronic Systems
External co-authors :
yes
Language :
English
Title :
Extended Adjacency and Scale-dependent Graph Fourier Transform via Diffusion Distances
Publication date :
2020
Journal title :
IEEE Transactions on Signal and Information Processing over Networks
ISSN :
2373-776X
Publisher :
Institute of Electrical and Electronics Engineers, New York, United States - New York
Peer reviewed :
Peer reviewed
Focus Area :
Security, Reliability and Trust
European Projects :
H2020 - 742648 - AGNOSTIC - Actively Enhanced Cognition based Framework for Design of Complex Systems
Funders :
CE - Commission Européenne [BE]
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since 06 August 2020

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