The application of localisation to near infrared calibration and prediction through partial least squares regression

Near infrared (NIR) calibration and prediction represents a strategy for solving the inverse problem of determining the input sample property from its output NIR spectrum. The spectrum is an indirect measurement of the property that has been smoothed, leading to a loss of information. As a result, small changes in the spectra can, on occasions, correspond to large changes in the property. However, the well-established mathematical theory of regularisation has been developed for the solution of indirect measurement and inverse problems. Regularisation seeks an approximation to the input that simultaneously forces the model output to agree closely with the observed output and guarantees that appropriate constraints about the behaviour of the input are satisfied. In partial least squares regression, this is achieved through the simultaneous fitting of a model to the measured spectra and another to the property data, with the models coupled through the same set of regression factors. It is this idea that must be carried over to localisation in order to transform it into a stabilised algorithm. In other words, localisation should be carried out with respect to both the spectrum and the property. This paper presents a theoretical basis for this concept together with the results of simulation experiments that compares the effects of localisation with respect to both the spectra and the property with spectrum only and property only localisation.