DocumentCode
2723095
Title
Near Optimal Column-Based Matrix Reconstruction
Author
Boutsidis, Christos ; Drineas, Petros ; Magdon-Ismail, Malik
Author_Institution
T.J. Watson Res. Center, Math. Sci. Dept., IBM, Yorktown Heights, NY, USA
fYear
2011
fDate
22-25 Oct. 2011
Firstpage
305
Lastpage
314
Abstract
We consider low-rank reconstruction of a matrix using a subset of its columns and we present asymptotically optimal algorithms for both spectral norm and Frobenius norm reconstruction. The main tools we introduce to obtain our results are: (i) the use of fast approximate SVD-like decompositions for column-based matrix reconstruction, and (ii) two deterministic algorithms for selecting rows from matrices with orthonormal columns, building upon the sparse representation theorem for decompositions of the identity that appeared in [1].
Keywords
singular value decomposition; sparse matrices; Frobenius norm; fast approximate SVD like decompositions; near optimal column based matrix reconstruction; orthonormal columns; sparse representation theorem; spectral norm; Accuracy; Approximation algorithms; Approximation methods; Matrix decomposition; Sparse matrices; Symmetric matrices; Vectors; SVD; approximate SVD; low-rank matrix approximation; spectral sparsification; subset selection;
fLanguage
English
Publisher
ieee
Conference_Titel
Foundations of Computer Science (FOCS), 2011 IEEE 52nd Annual Symposium on
Conference_Location
Palm Springs, CA
ISSN
0272-5428
Print_ISBN
978-1-4577-1843-4
Type
conf
DOI
10.1109/FOCS.2011.21
Filename
6108189
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