Lower rank approximation of matrices by least squares with any choice of weights

K. Ruben Gabriel*, S. Zamir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

219 Scopus citations

Abstract

Reduced rank approximation of matrices has hitherto been possible only by unweighted least squares. This paper presents iterative techniques for obtaining such approximations when weights are introduced. The techniques involve criss-cross regressions with careful initialization. Possible applications of the approximation are in modelling, biplotting, contingency table analysis, fitting of missing values, checking outliers, etc.

Original languageEnglish
Pages (from-to)489-498
Number of pages10
JournalTechnometrics
Volume21
Issue number4
DOIs
StatePublished - Nov 1979

Keywords

  • Biplot
  • Contingency table
  • Criss-cross regression
  • Householder-Young theorem
  • Least squares
  • Outliers
  • Reduced rank approximation

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