Wavelets on graphs via spectral graph theory - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Applied and Computational Harmonic Analysis Year : 2011

Wavelets on graphs via spectral graph theory

Abstract

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the graph analogue of the Fourier domain, namely the spectral decomposition of the discrete graph Laplacian L. Given a wavelet generating kernel g and a scale parameter t, we define the scaled wavelet operator Ttg = g(tL). The spectral graph wavelets are then formed by localizing this operator by applying it to an indicator function. Subject to an admissibility condition on g, this procedure defines an invertible transform. We explore the localization properties of the wavelets in the limit of fine scales. Additionally, we present a fast Chebyshev polynomial approximation algorithm for computing the transform that avoids the need for diagonalizing L. We highlight potential applications of the transform through examples of wavelets on graphs corresponding to a variety of different problem domains.
Fichier principal
Vignette du fichier
hammond-vandergheynst-gribonval-acha-2009r.pdf (2.7 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

inria-00541855 , version 1 (06-02-2011)

Identifiers

Cite

David K. Hammond, Pierre Vandergheynst, Rémi Gribonval. Wavelets on graphs via spectral graph theory. Applied and Computational Harmonic Analysis, 2011, 30 (2), pp.129--150. ⟨10.1016/j.acha.2010.04.005⟩. ⟨inria-00541855⟩
1472 View
5609 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More