PLS calibration

In the original PLS, the matrices T (scores), P (loadings) and the vector b are computed sequentially in the following way  

In the standard PLS algorithm wi, is normalised to unity length and subsequently, t ,i is calculated as 

This can be interpreted as one ALS iteration. If the iterations are continued, this process converges to the first eigenvector u ,i. The PLS compromise is to stop at one iteration. 

The function PLS ca librat ion, m is the PLS equivalent to PCR calibration, m. The iterative loop implements equations (5.73)-(5.77). The prognostic vector vprog is introduced in the next section. 

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The PLS calibration set was built mixing in an agate mortar different amounts of Mancozeb standard with kaolin, a coadjuvant usually formulated in agrochemicals. Cluster analysis was employed for sample classification and to select the adequate PLS model acording with the characteristics of the sample matrix and the presence of other components. 

MONITORIZATION OF Ca(OH), CONTENT IN ANHYDRITE, SUBPRODUCT OF HF PRODUCTION PROCESS, BY FT-IR SPECTROSCOPY USING PLS CALIBRATION METHOD... 

For our discussions, we have been using PLS to generate calibrations for all components simultaneously. Unlike PCR, it can often be advantageous to generate PLS calibrations for one component at a time. This allows PLS to find the best compromise factors for each individual component by ignoring the compromises that would be needed to accomodate the other components. When PLS is used to calibrate multiple components simultaneously, it is often called PLS-2. When used to generate calibrations for one component at a time it is often called PLS-1. 

Whether this tendency of PLS to reject nonlinearities by pushing them onto the later factors which are usually discarded as noise factors will improve or degrade the prediction accuracy and robustness of a PLS calibration as compared to the same calibration generated by PCR depends very much upon the specifics of the data and the application. If the nonlinearities are poorly correlated to the properties which we are trying to predict, rejecting them can improve the accuracy. On the other hand, if the rejected nonlinearities contain information that has predictive value, then the PLS calibration may not perform as well as the corresponding PCR calibration that retains more of the nonlinearities and therefore is able to exploit the information they contain. In short, the only sure way to determine if PLS or PCR is better for a given calibration is to try both of them and compare the results. 

PLSPRESS13 PLSPRESS23 PRESS of PLS calibration from AI/C1 for A3 PRESS of PLS calibration from A2/C2 for A3... 

PLSlcal PLS2cal PLS calibration coefficients from Al/Cl PLS calibration coefficients from A2/C2... 

PLSlres PLS13res PLS14res PLSISres PLS calibration from Al/Cl predicts concentrations for Al PLS calibration from Al/Cl predicts concentrations for A3 PCR calibration from Al/Cl predicts concentrations for A4 PCR calibration from Al/Cl predicts concentrations for A3... 

PLS2res PLS23res PLS24res PLS25res PLS calibration from A2/C2 predicts concentrations for A2 PLS calibration from A2/C2 predicts concentrations for A3 PLS calibration from A2/C2 predicts concentrations for A4 PLS calibration from A2/C2 predicts concentrations for AS... 

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