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Dual‐ and triple‐mode matrix approximation and regression modelling
Author(s) -
Lipovetsky Stan,
Michael Conklin W.
Publication year - 2003
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.503
Subject(s) - singular value decomposition , interpretation (philosophy) , regression , mathematics , regression analysis , matrix (chemical analysis) , robust regression , total least squares , dual (grammatical number) , set (abstract data type) , principal component regression , computer science , statistics , algorithm , art , materials science , literature , composite material , programming language
We propose a dual‐ and triple‐mode least squares for matrix approximation. This technique applied to the singular value decomposition produces the classical solution with a new interpretation. Applied to regression modelling, this approach corresponds to a regularized objective and yields a new solution with properties of a ridge regression. The results for regression are robust and suggest a convenient tool for the analysis and interpretation of the model coefficients. Numerical results are given for a marketing research data set. Copyright © 2003 John Wiley & Sons, Ltd.