Local centering in multivariate calibration

Abstract

Multivariate calibration models are constructed using measured responses of variables (e.g. spectra) on a set of calibration samples and values of a quantity of interest (e.g. concentration) measured by a reference method. The goal is to replace the reference method. Traditionally the calibration data are mean centered, which insures minimum average prediction error (for a prediction set having the same distribution as the calibration set). An alternative to this preliminary data treatment is presented. Instead of using the entire calibration set for centering, a subset of samples from the calibration set that are closest to the unknown is selected for centering. This preliminary data treatment reduces reliance on regression. Thus it is expected to perform well in cases where model errors are dominating or extrapolation occurs. The method is tested on data from near-infrared reflectance and infrared emission spectroscopy, showing that an average improvement of 20% in prediction accuracy is achievable. This method is fundamentally different from locally weighted regression because it uses the entire calibration set for the regression step.