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Comparison of simple projection methods (OPLS, PLSO, and TP) for separation of predicting and non‐predicting information in PLSR and PCR, with focus on DA
Author(s) -
Ergon Rolf
Publication year - 2014
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.2649
Subject(s) - partial least squares regression , principal component analysis , opls , projection (relational algebra) , linear discriminant analysis , mathematics , similarity (geometry) , pattern recognition (psychology) , simple (philosophy) , artificial intelligence , statistics , computer science , chemistry , algorithm , philosophy , epistemology , image (mathematics) , hydrogen bond , organic chemistry , molecule
Orthogonal projections to latent structures (OPLS) and target projection (TP) are two alternative methods for separation of predicting and non‐predicting parts of the predictor matrix in partial least squares regression (PLSR), which can also be applied on principal component regression (PCR). An additional new method called PLSO is developed in the paper. In all three methods, the predicting score vector is a scaled version of the fitted response vector. Otherwise, the resulting score and loading vectors are different, although OPLS and TP are identical within similarity transformations. All these relations are here found by simple projections of the fitted predictor matrix from PLSR or PCR, and the similarities and differences are illustrated in discriminant analysis examples. Copyright © 2014 John Wiley & Sons, Ltd.