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PCR/PLSR optimization based on noise covariance estimation and Kalman filtering theory
Author(s) -
Ergon Rolf,
Esbensen Kim H.
Publication year - 2002
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.732
Subject(s) - partial least squares regression , kalman filter , covariance , latent variable , principal component regression , noise (video) , statistics , extension (predicate logic) , ordinary least squares , computer science , mathematics , principal component analysis , algorithm , mathematical optimization , artificial intelligence , image (mathematics) , programming language
The theoretical connection between principal component regression (PCR) and partial least squares regression (PLSR) on one hand and Kalman filtering (KF) on the other is known from earlier work. In the present paper we investigate the possibilities to use latent variables modeling and KF theory as means for optimization of ordinary PLSR and PCR predictors, based on the prerequisite of prior X noise covariance estimates facilitated e.g. by more X than y observations. The result is a new PLSR optimization method, while the PCR optimization turns out to be identical with an earlier known method. A simulation example and two real‐world data examples supporting the theoretical development are presented. The treatment is limited to cases with only one response variable, although an extension to multiresponse cases is also possible. Copyright © 2002 John Wiley & Sons, Ltd.