• 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