Change search
ReferencesLink to record
Permanent link

Direct link
Stability of Two Direct Methods for Bidiagonalization and Partial Least Squares
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
2014 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 35, no 1, 279-291 p.Article in journal (Refereed) Published
Abstract [en]

The partial least squares (PLS) method computes a sequence of approximate solutions x(k) is an element of K-k (A(T) A, A(T) b), k = 1, 2, ..., to the least squares problem min(x) parallel to Ax - b parallel to(2). If carried out to completion, the method always terminates with the pseudoinverse solution x(dagger) = A(dagger)b. Two direct PLS algorithms are analyzed. The first uses the Golub-Kahan Householder algorithm for reducing A to upper bidiagonal form. The second is the NIPALS PLS algorithm, due to Wold et al., which is based on rank-reducing orthogonal projections. The Householder algorithm is known to be mixed forward-backward stable. Numerical results are given, that support the conjecture that the NIPALS PLS algorithm shares this stability property. We draw attention to a flaw in some descriptions and implementations of this algorithm, related to a similar problem in Gram-Schmidt orthogonalization, that spoils its otherwise excellent stability. For large-scale sparse or structured problems, the iterative algorithm LSQR is an attractive alternative, provided an implementation with reorthogonalization is used.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2014. Vol. 35, no 1, 279-291 p.
Keyword [en]
partial least squares; bidiagonalization; core problem; stability; regression; NIPALS; Householder reflector; modified Gram-Schmidt orthogonalization
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-106303DOI: 10.1137/120895639ISI: 000333693300013OAI: diva2:715704
Available from: 2014-05-06 Created: 2014-05-05 Last updated: 2014-05-13Bibliographically approved

Open Access in DiVA

fulltext(290 kB)222 downloads
File information
File name FULLTEXT01.pdfFile size 290 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Björck, Åke
By organisation
Computational MathematicsThe Institute of Technology
In the same journal
SIAM Journal on Matrix Analysis and Applications
Natural Sciences

Search outside of DiVA

GoogleGoogle Scholar
Total: 222 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 89 hits
ReferencesLink to record
Permanent link

Direct link