On the PLS algorithm for multiple regression (PLS1)

Yoshio Takane, Sebastien Loisel

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Partial least squares (PLS) was first introduced byWold in the mid 1960s as a heuristic algorithm to solve linear least squares (LS) problems. No optimality property of the algorithm was known then. Since then, however, a number of interesting properties have been established about the PLS algorithm for regression analysis (called PLS1). This paper shows that the PLS estimator for a specific dimensionality S is a kind of constrained LS estimator confined to a Krylov subspace of dimensionality S. Links to the Lanczos bidiagonalization and conjugate gradient methods are also discussed from a somewhat different perspective from previous authors.

Original languageEnglish
Title of host publicationThe Multiple Facets of Partial Least Squares and Related Methods
PublisherSpringer
Pages17-28
Number of pages12
ISBN (Electronic)9783319406435
ISBN (Print)9783319406411
DOIs
Publication statusPublished - 16 Oct 2016

Publication series

NameSpringer Proceedings in Mathematics & Statistics
PublisherSpringer
Volume173
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Fingerprint

Partial Least Squares
Least Square Algorithm
Multiple Regression
Least Squares Estimator
Dimensionality
Constrained Least Squares
Lanczos
Linear Least Squares
Krylov Subspace
Least Squares Problem
Conjugate Gradient Method
Regression Analysis
Heuristic algorithm
Optimality

Keywords

  • Conjugate gradients
  • Constrained principal component analysis (CPCA)
  • Krylov subspace
  • Lanczos bidiagonalization
  • NIPALS
  • PLS1 algorithm

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Takane, Y., & Loisel, S. (2016). On the PLS algorithm for multiple regression (PLS1). In The Multiple Facets of Partial Least Squares and Related Methods (pp. 17-28). (Springer Proceedings in Mathematics & Statistics; Vol. 173). Springer. https://doi.org/10.1007/978-3-319-40643-5_2
Takane, Yoshio ; Loisel, Sebastien. / On the PLS algorithm for multiple regression (PLS1). The Multiple Facets of Partial Least Squares and Related Methods. Springer, 2016. pp. 17-28 (Springer Proceedings in Mathematics & Statistics).
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Takane, Y & Loisel, S 2016, On the PLS algorithm for multiple regression (PLS1). in The Multiple Facets of Partial Least Squares and Related Methods. Springer Proceedings in Mathematics & Statistics, vol. 173, Springer, pp. 17-28. https://doi.org/10.1007/978-3-319-40643-5_2

On the PLS algorithm for multiple regression (PLS1). / Takane, Yoshio; Loisel, Sebastien.

The Multiple Facets of Partial Least Squares and Related Methods. Springer, 2016. p. 17-28 (Springer Proceedings in Mathematics & Statistics; Vol. 173).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Takane Y, Loisel S. On the PLS algorithm for multiple regression (PLS1). In The Multiple Facets of Partial Least Squares and Related Methods. Springer. 2016. p. 17-28. (Springer Proceedings in Mathematics & Statistics). https://doi.org/10.1007/978-3-319-40643-5_2