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Lower Rank Approximation of Matrices by Least Squares With Any Choice of Weights

 

作者: K.Ruben Gabriel,   S. Zamir,  

 

期刊: Technometrics  （Taylor Available online 1979）
卷期: Volume 21, issue 4  

页码: 489-498

 

ISSN:0040-1706

 

年代: 1979

 

DOI:10.1080/00401706.1979.10489819

 

出版商: Taylor & Francis Group

 

关键词: Reduced rank approximation;Least squares;Criss-cross regression;Householder-Young theorem;Biplot;Contingency table;Outliers

 

数据来源: Taylor

 

摘要:

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.

 

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