Constructing fast approximate eigenspaces with application to the fast graph Fourier transforms

Abstract

We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider extended orthogonal Givens or scaling and shear transformations). The number of these components controls the trade-off between approximation accuracy and the computational complexity of projecting on the eigenspaces. We write minimization problems for the single fundamental components and provide closed-form solutions. Then we propose algorithms that iterative update all these components until convergence. We show results on random matrices and an application on the approximation of graph Fourier transforms for directed and undirected graphs.

References in corpus (6)

• On the Graph Fourier Transform for Directed Graphs
• Treelets--An adaptive multi-scale basis for sparse unordered data
• Approximate fast graph Fourier transforms via multi-layer sparse approximations
• Learning Fast Sparsifying Transforms
• Approximating Orthogonal Matrices with Effective Givens Factorization
• Asymmetric Multiresolution Matrix Factorization

Cited by in corpus (1)

• An iterative coordinate descent algorithm to compute sparse low-rank approximations