Near-Optimal Column-Based Matrix Reconstruction
Data Structures and Algorithms
2015-03-19 v3
Abstract
We consider low-rank reconstruction of a matrix using its columns and we present asymptotically optimal algorithms for both spectral norm and Frobenius norm reconstruction. The main tools we introduce to obtain our r esults are: (i) the use of fast approximate SVD-like decompositions for column reconstruction, and (ii) two deter ministic algorithms for selecting rows from matrices with orthonormal columns, building upon the sparse represen tation theorem for decompositions of the identity that appeared in \cite{BSS09}.
Cite
@article{arxiv.1103.0995,
title = {Near-Optimal Column-Based Matrix Reconstruction},
author = {Christos Boutsidis and Petros Drineas and Malik Magdon-Ismail},
journal= {arXiv preprint arXiv:1103.0995},
year = {2015}
}
Comments
SIAM Journal on Computing (SICOMP), invited to special issue of FOCS 2011