Article

A theoretical foundation for the PLS algorithm

  1. Avraham Lorber†,
  2. Lawrence E. Wangen‡,
  3. Bruce R. Kowalski

Article first published online: 30 MAR 2005

DOI: 10.1002/cem.1180010105

Issue

Journal of Chemometrics

Journal of Chemometrics

Volume 1, Issue 1, pages 19–31, January 1987

Additional Information

How to Cite

Lorber, A., Wangen, L. E. and Kowalski, B. R. (1987), A theoretical foundation for the PLS algorithm. Journal of Chemometrics, 1: 19–31. doi: 10.1002/cem.1180010105

Author Information

  1. Center for Process Analytical Chemistry, and Laboratory for Chemometrics, Department of Chemistry BG-10, University of Washington, Seattle, Washington 98195, U.S.A.

  1. †

    Nuclear Research Centre — Negev, P.O. Box 9001, Beer-Sheva 84190, Israel.

  2. ‡

    Analytical Chemistry Group, Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A.

Publication History

  1. Issue published online: 30 MAR 2005
  2. Article first published online: 30 MAR 2005
  3. Manuscript Revised: 15 AUG 1986
  4. Manuscript Received: 1 JUL 1986

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Keywords:

  • Calibration;
  • Indirect calibration;
  • Multivariate;
  • Matrix decomposition;
  • PLS;
  • PCR

Abstract

Partial least squares (PLS) modeling is an algorithm for relating one or more dependent variables to two or more independent variables. As a regression procedure it apparently evolved from the method of principal components regression (PCR) using the NIPALS algorithm, which is similar to the power method for determining the eigenvectors and eigenvalues of a matrix. This paper presents a theoretical explanation of the PLS algorithm using singular value decomposition and the power method. The relation of PLS to PCR is demonstrated, and PLS is shown to be one of a continuum of possible solutions of a similar type. These other solutions may give better prediction than either PLS or PCR under appropriate conditions.

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