The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
A theoretical foundation for the PLS algorithm
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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Citations
Cites
Wold, S., Ruhe, A., Wold, H., & Dunn, III (1984) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0905052 · Cited by 2,529
Cited by
SIMPLS: An alternative approach to partial least squares regression
de Jong, S. (1993) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/0169-7439(93)85002-x · Cited by 1,905
Multivariate statistical monitoring of process operating performance
Kresta, J. V., Macgregor, J. F., & Marlin, T. E. (1991) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.5450690105 · Cited by 989
ter Braak, C. J. F., & Juggins, S. (1993) · Twelfth International Diatom Symposium · doi:10.1007/978-94-017-3622-0_49 · Cited by 785
On the structure of partial least squares regression
Helland, I. S. (1988) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918808812681 · Cited by 559
Wold, S., Kettaneh-Wold, N., & Skagerberg, B. (1989) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/0169-7439(89)80111-x · Cited by 532
Metadata
- Authors
- Lorber, A., Wangen, L. E., & Kowalski, B. R.
- Venue
- Journal of Chemometrics
- Publisher
- Wiley
- Published
- 1987-01
- Volume
- 1
- Issue
- 1
- Pages
- 19-31
- ISSN
- 0886-9383 (ISSN-L)
- 1099-128X
- OpenAlex
- W2058382695
- Cited by
- 449
- References
- 1
- FWCI
- 27.50
- Type
- journal article
- Language
- en
- Open access
- closed
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- Lorber, A., Wangen, L. E., & Kowalski, B. R. (1987). A theoretical foundation for the PLS algorithm. Journal of Chemometrics. https://doi.org/10.1002/cem.1180010105
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
