Work

Near-Optimal Column-Based Matrix Reconstruction

Year: 2011

Type: preprint

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}.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1103.0995

Authors: Boutsidis, Christos, Drineas, Petros, Magdon-Ismail, Malik

Institutions: IBM Research - Thomas J. Watson Research Center, Rensselaer Polytechnic Institute

Language: English

Topic: Sparse and Compressive Sensing Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Defense Advanced Research Projects Agency, Advanced Research Projects Agency

Awards: AF: Small: Fast and Efficient Randomized Algorithms for Solving Laplacian Systems of Linear Equations and Sparse Least Squares Problems, Collaborative Research: Randomized Algorithms in Linear Algebra and Numerical Evaluations on Massive Datasets, G4096326766, G4713059963

OpenAlex ID: W2950024299

Cites: 22

Cited by: 62

Related to: 20