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Grassmann algorithms for low rank approximation of matrices with missing values
Linköping University, Department of Mathematics, Scientific Computing. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Scientific Computing. Linköping University, The Institute of Technology.ORCID iD: 0000-0003-2281-856X
2010 (English)In: BIT NUMERICAL MATHEMATICS, ISSN 0006-3835, Vol. 50, no 1, 173-191 p.Article in journal (Refereed) Published
Abstract [en]

The problem of approximating a matrix by another matrix of lower rank, when a modest portion of its elements are missing, is considered. The solution is obtained using Newtons algorithm to find a zero of a vector field on a product manifold. As a preliminary the algorithm is formulated for the well-known case with no missing elements where also a rederivation of the correction equation in a block Jacobi-Davidson method is included. Numerical examples show that the Newton algorithm grows more efficient than an alternating least squares procedure as the amount of missing values increases.

Place, publisher, year, edition, pages
2010. Vol. 50, no 1, 173-191 p.
Keyword [en]
Grassmann manifold, Matrix, Low rank approximation, Newtons method, Singular value decomposition, Least squares, Missing values
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-54404DOI: 10.1007/s10543-010-0253-9ISI: 000274956300010OAI: oai:DiVA.org:liu-54404DiVA: diva2:303523
Note
The final publication is available at www.springerlink.com: Lennart Simonsson and Lars Elden, Grassmann algorithms for low rank approximation of matrices with missing values, 2010, BIT NUMERICAL MATHEMATICS, (50), 1, 173-191. http://dx.doi.org/10.1007/s10543-010-0253-9 Copyright: Springer Science Business Media http://www.springerlink.com/ Available from: 2010-03-12 Created: 2010-03-12 Last updated: 2013-08-30

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Simonsson, LennartElden, Lars

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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  • Other style
More styles
Language
  • de-DE
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  • sv-SE
  • Other locale
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Output format
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