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Multiresolution analysis of functions on directed networks
Author(s): Harry Sevi; Gabriel Rilling; Pierre Borgnat
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Paper Abstract

We introduce a novel design for analyzing and approximating functions defined on the vertices of a directed graph Γ in a multi-scale fashion. The starting point of our construction is the setting-up of a frequency notion through the study of the Dirichlet energy of random walk operator's eigenfunctions. By this alluring frequency interpretation, the set of random walk's eigenfunctions is considered as the Fourier basis for functions over directed graphs. We are thus able to construct a multi-scale frame based on the bi-orthogonal basis of the random walk on directed graphs. This multi-resolution frame paves thus the way to a generalization of the diffusion wavelet framework to the directed scope.

Paper Details

Date Published: 21 September 2017
PDF: 14 pages
Proc. SPIE 10394, Wavelets and Sparsity XVII, 103941Q (21 September 2017); doi: 10.1117/12.2274341
Show Author Affiliations
Harry Sevi, CEA, LIST, Lab. d'Analyse de Donné et Intelligence des Systèmes (France)
Univ. Lyon, Ens de Lyon, UCB Lyon 1, Lab. de Physique, CNRS (France)
Gabriel Rilling, CEA, LIST, Lab. d'Analyse de Donné et Intelligence des Systèmes (France)
Pierre Borgnat, Univ. Lyon, Ens de Lyon, UCB Lyon 1, Lab. de Physique, CNRS (France)


Published in SPIE Proceedings Vol. 10394:
Wavelets and Sparsity XVII
Yue M. Lu; Dimitri Van De Ville; Manos Papadakis, Editor(s)

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