Einleitung

Nonlinear multivariate calibration methods in analytical chemistry

“…With emphasis now shifting to the ability to model nonlinear information, several tech-niques have been adapted or created to deal with such information, including locally weighted regression (LWR), projection pursuit regression (PPR), alternating conditional expectations (ACE), multivariate adaptive regression splines (MARS), and neural networks (NN). PCR and PLS can also be used to describe nonlinear systems by either incorporating a larger number of latent variables than would be required for a linear system (12) or using the nonlinear or quadratic versions of the algorithms (13,14). Whatever the method origin, each of these techniques aims at describing the nonlinear relationship that exists between a given sample attribute (in analytical chemistry this is most often solute concentration) and its measured instrument responses.…”

“…In Equation 6the augmented scores matrix contains the first two score vectors and their quadratic transforms. This is the approach adopted here, although other algo rithms are available for the PLS method that also enable incorporation of interaction terms (such as t1> t2) (13).…”

“…By correctly identifying the subregions and the associated significant variables, it is possible to obtain linear or cubic spline estimates of the observed functionality for individual subregions. The entire model can be simply stated as c = fl(R) + e (13) where c contains the sample concentration information, R is the instrument response matrix, f refers to the nonlinear functionality of the data, and e refers to the concentration residuals.…”

Nonlinear Multivariate Calibration Methods in Analytical Chemistry

“…With emphasis now shifting to the ability to model nonlinear information, several tech-niques have been adapted or created to deal with such information, including locally weighted regression (LWR), projection pursuit regression (PPR), alternating conditional expectations (ACE), multivariate adaptive regression splines (MARS), and neural networks (NN). PCR and PLS can also be used to describe nonlinear systems by either incorporating a larger number of latent variables than would be required for a linear system (12) or using the nonlinear or quadratic versions of the algorithms (13,14). Whatever the method origin, each of these techniques aims at describing the nonlinear relationship that exists between a given sample attribute (in analytical chemistry this is most often solute concentration) and its measured instrument responses.…”

“…In Equation 6the augmented scores matrix contains the first two score vectors and their quadratic transforms. This is the approach adopted here, although other algo rithms are available for the PLS method that also enable incorporation of interaction terms (such as tp t2) (13).…”