Multivariate spectroscopic calibration models are only valid to predict samples within the span of the calibration sample space measured relative to the current instrument environment (the primary conditions). Predicting samples in secondary conditions with new variances, same sample variances as the calibration space but a new instrument environment, or both, requires some form of continual model maintenance and/or transfer. Previous work has shown that a Tikhonov regularization (TR) approach is capable of accomplishing both tasks by updating the primary model based on only a few samples (transfer or standardization set) measured under the secondary conditions. A distinction of the TR design for calibration maintenance and transfer is a defined weighting scheme for the small set of standardization samples augmented to the full set of primary calibration samples. Critical to successful calibration maintenance or transfer is the standardization sample set composition, i.e. standardization samples should properly represent that are less secondary conditions. This paper reports on using TR-based methods to investigate this issue and a consensus modeling approach is briefly evaluated.
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.
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