Fast Multiscale Diffusion on Graphs

Sibylle Marcotte (1, 2) , Amélie Barbe (2) , Rémi Gribonval (2) , Titouan Vayer (2) , Marc Sebban (3) , Pierre Borgnat (4) , Paulo Gonçalves (2)

1 ENS Rennes - École normale supérieure - Rennes
2 DANTE - Réseaux dynamiques : approche structurelle et temporelle
3 LHC - Laboratoire Hubert Curien
4 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

Diffusing a graph signal at multiple scales requires computing the action of the exponential of several multiples of the Laplacian matrix. We tighten a bound on the approximation error of truncated Chebyshev polynomial approximations of the exponential, hence significantly improving a priori estimates of the polynomial order for a prescribed error. We further exploit properties of these approximations to factorize the computation of the action of the diffusion operator over multiple scales, thus reducing drastically its computational cost.

Mots clés: Approximate computing; Chebyshev approximation; Computational efficiency; Estimation error; Polynomials

Domaines: Traitement du signal et de l'image [eess.SP]; Analyse numérique [math.NA]; Analyse numérique [cs.NA]

Sibylle Marcotte, Amélie Barbe, Rémi Gribonval, Titouan Vayer, Marc Sebban, et al.. Fast Multiscale Diffusion on Graphs. ICASSP 2022 - IEEE International Conference on Acoustics, Speech and Signal Processing, May 2022, Singapore, Singapore. ⟨10.1109/ICASSP43922.2022.9746802⟩. ⟨hal-03212764v2⟩