Perturbations of CUR Decompositions
Numerical Analysis
2020-07-29 v2 Numerical Analysis
Abstract
The CUR decomposition is a factorization of a low-rank matrix obtained by selecting certain column and row submatrices of it. We perform a thorough investigation of what happens to such decompositions in the presence of noise. Since CUR decompositions are non-uniquely formed, we investigate several variants and give perturbation estimates for each in terms of the magnitude of the noise matrix in a broad class of norms which includes all Schatten --norms. The estimates given here are qualitative and illustrate how the choice of columns and rows affects the quality of the approximation, and additionally we obtain new state-of-the-art bounds for some variants of CUR approximations.
Keywords
Cite
@article{arxiv.1908.08101,
title = {Perturbations of CUR Decompositions},
author = {Keaton Hamm and Longxiu Huang},
journal= {arXiv preprint arXiv:1908.08101},
year = {2020}
}