Analyzing the Approximation Error of the Fast Graph Fourier Transform

The graph Fourier transform (GFT) is in general dense and requires O(n²⁾ time to compute and O(n²⁾ 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.