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Partial least squares discriminant analysis for chemometrics and metabolomics: H ow scores, loadings, and weights differ according to two common algorithms
Author(s) -
Brereton Richard G.,
Lloyd Gavin R.
Publication year - 2018
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.3028
Subject(s) - mathematics , linear discriminant analysis , chemometrics , partial least squares regression , algorithm , variable (mathematics) , discriminant , statistics , rotation (mathematics) , least squares function approximation , pattern recognition (psychology) , artificial intelligence , computer science , geometry , machine learning , mathematical analysis , estimator
Two common algorithms for partial least squares discriminant analysis developed by Wold (NIPALS) and by Martens are compared. Although their classification performance is identical, their projections into variable space (often called scores) and into object space (loadings and weights) are quite different. Martens' algorithm can be visualised as a rotation in variable space, but Wold's results in quite complex distortions. Most software presents scores plots using the Wold algorithm but fails to appreciate that variable space is distorted, so scores from both algorithms are different. Weights, which can be obtained from both methods, are identical, although loadings (as commonly defined) from the Wold algorithm differ. The paper illustrates the two methods graphically to review the difference between these two methods.