Spectral Multivariate Calibration with Wavelength Selection Using Variants of Tikhonov Regularization

Abstract

Tikhonov regularization (TR) is a general method that can be used to form a multivariate calibration model and numerous variants of it exist, including ridge regression (RR). This paper reports on the unique flexibility of TR to form a model using full wavelengths (RR), individually selected wavelengths, or multiple bands of selected wavelengths. Of these three TR variants, the one based on selection of wavelength bands is found to produce lower prediction errors. As with most wavelength selection algorithms, the model vector magnitude indicates that this error reduction comes with a potential increase in prediction uncertainty. Results are presented for near-infrared, ultraviolet–visible, and synthetic spectral data sets. While the focus of this paper is wavelength selection, the TR methods are generic and applicable to other variable-selection situations.