# Constructing Fast Approximate Eigenspaces With Application to the Fast Graph Fourier Transforms

@article{Rusu2021ConstructingFA, title={Constructing Fast Approximate Eigenspaces With Application to the Fast Graph Fourier Transforms}, author={Cristian Rusu and Lorenzo Rosasco}, journal={IEEE Transactions on Signal Processing}, year={2021}, volume={69}, pages={5037-5050} }

We investigate numerically efficient approximations of eigenspaces associated with symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated which we consider to be 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…

## 2 Citations

An iterative Jacobi-like algorithm to compute a few sparse eigenvalue-eigenvector pairs

- Mathematics, Computer ScienceArXiv
- 2021

A new algorithm to compute the extreme eigenvalue/eigenvector pairs of a symmetric matrix and shows applications to random symmetric matrices, graph Fourier transforms, and with the sparse principal component analysis in image classification experiments.

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

- Computer Science, EngineeringIEEE Signal Processing Letters
- 2021

The proposed algorithm can be viewed as an extension of the Kogbetliantz algorithm to build an approximate singular value decomposition for a few principal components and perform dimensionality reduction for classification applications.

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