Spectroscopic prediction of nonlinear properties by principal component regression

The Principal Component Regression method is widely used in analytical spectroscopy, even for prediction of nonlinear or almost nonlinear properties. This study analyzes the error introduced by the nonlinearity, as compared to common factors such as experimental noise level and spectral characteristics (e.g. overlapping). It has been found that nonlinearities are responsible for the major contribution to the final prediction errors. A simple algorithm to handle such nonlinearities and to significantly improve PCR prediction results is proposed and evaluated. It is based on a spectral transformation that partially compensates for the nonlinearity. The transformation is simple and is unique for the whole spectrum. Numerous simulations show that this algorithm considerably improves linear PCR predictions and is comparable to more complicated common nonlinear calibrations. Its performance is best when the nonlinear functional form (connecting concentrations to the predicted properties) is known, however, an algorithm to handle unknown functions is also provided. Moreover, this method may be applied for investigating the functional forms and a simple example for this mode of the algorithm is given. The algorithm is exemplified by its application to experimental data: It is applied to improve PCR prediction of electrical conductivity from spectral information, in a system of acetic acid and acetone solutions.