I. Litanibarzilai et I. Schechter, SPECTROSCOPIC PREDICTION OF NONLINEAR PROPERTIES BY PRINCIPAL COMPONENT REGRESSION, Analytica chimica acta, 348(1-3), 1997, pp. 345-356
The Principal Component Regression method is widely used in analytical
spectroscopy, even for prediction of nonlinear or almost nonlinear pr
operties. This study analyzes the error introduced by the nonlinearity
, as compared to common factors such as experimental noise level and s
pectral characteristics (e.g. overlapping). It has been found that non
linearities are responsible for the major contribution to the final pr
ediction errors. A simple algorithm to handle such nonlinearities and
to significantly improve PCR prediction results is proposed and evalua
ted. It is based on a spectral transformation that partially compensat
es for the nonlinearity. The transformation is simple and is unique fo
r the whole spectrum. Numerous simulations show that this algorithm co
nsiderably improves linear PCR predictions and is comparable to more c
omplicated common nonlinear calibrations. Its performance is best when
the nonlinear functional form (connecting concentrations to the predi
cted properties) is known, however, an algorithm to handle unknown fun
ctions is also provided. Moreover, this method may be applied for inve
stigating the functional forms and a simple example for this mode of t
he algorithm is given. The algorithm is exemplified by its application
to experimental data: It is applied to improve PCR prediction of elec
trical conductivity from spectral information, in a system of acetic a
cid and acetone solutions.