Partial least-squares (PLS) regression is a very widely used technique in s
pectroscopy for calibration/prediction purposes. One of the most important
steps in the application of the PLS regression is the determination of the
correct number of dimensions to use in order to avoid over-fitting, and the
refore to obtain a robust predictive model. The "structured" nature of spec
troscopic signals may be used in several ways as a guide to improve the PLS
models. The aim of this work is to propose a new technique for the applica
tion of PLS regression to signals (FT-IR, NMR, etc.). This technique is bas
ed on the Savitsky-Golay (SG) smoothing of the loadings weights vectors (w)
obtained at each iteration step of the NIPALS procedure. This smoothing pr
ogressively "displaces" the random or quasi-random variations from earlier
(most important) to later (less important) PLS latent variables. The Durbin
-Watson (DW) criterion is calculated for each PLS vectors (p, w, b) at each
iteration step of the smoothed NIPALS procedure in order to measure the ev
olution of their "noise" content. PoLiSh has been applied to simulated data
sets with different noise levels and it was found that for those with noise
levels higher than 10-20%, an improvement in the predictive ability of the
models is observed. This technique is also important as a tool to evaluate
the true dimensionality of signal matrices for complex PLS models, by comp
aring the DW profile of the PoLiSh vectors at different smoothing degrees w
ith those of the unsmoothed PLS models. (C) 2001 Elsevier Science B.V. All
rights reserved.