Reference : Extended Adjacency and Scale-dependent Graph Fourier Transform via Diffusion Distances
Scientific journals : Article
Engineering, computing & technology : Electrical & electronics engineering
Security, Reliability and Trust
Extended Adjacency and Scale-dependent Graph Fourier Transform via Diffusion Distances
Elias, Vitor R.M. mailto []
Alves Martins, Wallace mailto [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > >]
Werner, Stefan mailto [Norwegian University of Science and Technology (NTNU) > Department of Electronic Systems]
IEEE Transactions on Signal and Information Processing over Networks
Institute of Electrical and Electronics Engineers
New York
[en] diffusion distances ; diffusion maps ; extended adjacency ; graph signal processing ; scale-dependent graph Fourier transform
[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.
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2020 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 — authors’ preprint of paper published in the IEEE Transactions on Signal and Information Processing over Networks.
H2020 ; 742648 - AGNOSTIC - Actively Enhanced Cognition based Framework for Design of Complex Systems

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