Analyzing the Approximation Error of the Fast Graph Fourier Transform

Luc Le Magoarou (1) , Nicolas Tremblay (2) , Rémi Gribonval (3)

1 IRT b-com - Institut de Recherche Technologique b-com
2 GIPSA-CICS - GIPSA - Communication Information and Complex Systems
3 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio

The graph Fourier transform (GFT) is in general dense and requires O(n 2) time to compute and O(n 2) memory space to store. In this paper, we pursue our previous work on the approximate fast graph Fourier transform (FGFT). The FGFT is computed via a truncated Jacobi algorithm, and is defined as the product of J Givens rotations (very sparse orthogonal matrices). The truncation parameter, J, represents a trade-off between precision of the transform and time of computation (and storage space). We explore further this trade-off and study, on different types of graphs, how is the approximation error distributed along the spectrum.

Domaines: Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]

Luc Le Magoarou, Nicolas Tremblay, Rémi Gribonval. Analyzing the Approximation Error of the Fast Graph Fourier Transform. ACSSC 2017 - 51st Annual Asilomar Conference on Signals Systems and Computers, Oct 2017, Monterey, California, United States. ⟨hal-01627434⟩