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Partial least-squares vs. Lanczos bidiagonalization—I: analysis of a projection method for multiple regression
Linköping University, Department of Mathematics, Scientific Computing. Linköping University, The Institute of Technology.ORCID iD: 0000-0003-2281-856X
2004 (English)In: Computational Statistics & Data Analysis, ISSN 0167-9473, E-ISSN 1872-7352, Vol. 46, no 1, 11-31 p.Article in journal (Refereed) Published
Abstract [en]

Multiple linear regression is considered and the partial least-squares method (PLS) for computing a projection onto a lower-dimensional subspace is analyzed. The equivalence of PLS to Lanczos bidiagonalization is a basic part of the analysis. Singular value analysis, Krylov subspaces, and shrinkage factors are used to explain why, in many cases, PLS gives a faster reduction of the residual than standard principal components regression. It is also shown why in some cases the dimension of the subspace, given by PLS, is not as small as desired.

Place, publisher, year, edition, pages
Elsevier, 2004. Vol. 46, no 1, 11-31 p.
Keyword [en]
partial least-squares; Lanczos bidiagonalization; singular value decomposition; principal components regression; Krylov subspace; chemometrics; shrinkage factors
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-22836DOI: 10.1016/S0167-9473(03)00138-5ISI: 000220929400002Local ID: 2174OAI: oai:DiVA.org:liu-22836DiVA: diva2:243149
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2017-12-13Bibliographically approved

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Eldén, Lars

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