Model Updating for Spectral Calibration Maintenance and Transfer Using 1-Norm Variants of Tikhonov Regularization

Abstract

In this study, calibration maintenance confronts the problem of updating a model developed in the primary condition to accurately predict the calibrated analyte in samples measured in new secondary conditions. Calibration transfer refers to updating a model based on a primary instrument to predict samples measured on new secondary instruments. A 2-norm variant of Tikhonov regularization (TR) has been used with spectroscopic data to perform calibration maintenance and transfer where just a few samples measured in the secondary condition/instrument are augmented to the primary calibration data to update the primary model. To achieve improved predictions, in this paper we report on 1-norm penalties to create two novel variants of TR for model updating. To solve the multiple penalty minimization numerical problems involved with the new TR variants, data transformation processes are applied, allowing a least absolute shrinkage and selection operator type algorithm to be implemented. Near-infrared spectra measured under two different temperatures represent the calibration maintenance application, and near-infrared spectra measured on two instruments denote the calibration transfer situation. Compared to TR in the recently developed 2-norm penalty mode, validation sample prediction errors are reduced when the 1-norm TR variant that selects wavelengths is used.

Impact of standardization sample design on Tikhonov regularization variants for spectroscopic calibration maintenance and transfer

“…The methods studied in this paper are three variants of Tikhonov regularization (TR) [24,25] used for calibration maintenance and transfer [26,27]. One of the TR variations is restricted to vector 2-norm minimizations [26] and the other two new adaptations of TR were recently developed to include 1-norm vector minimizations [27]. Results can improve with the 1-norm compared to those reported for TR in 2-norm.…”

Sparse Methods in Spectroscopy: An Introduction, Overview, and Perspective

“…7, we hope to immunize the primary calibration model against spectral noise while simultaneously performing wavelength selection. This augmentation forms the basis of many recent calibration transfer and maintenance methods [33][34][35] including augmented classical least-squares procedures, which decompose spectra into pure-component concentrations and pure-component spectra. [36][37][38][39][40] More recently, a comprehensive review of two-norm and one-norm penalties for sparse multivariate calibration and maintenance was undertaken by Kalivas.…”

Stacked PLS for calibration transfer without standards

“…Not surprisingly, the number of update samples needed to span the new effects, as well as their optimal placement in the calibration model, varies with the number of samples in the original calibration model and with the amount of correction required to make the model useful to predict on spectral responses from the secondary instrument. Previous work has shown that, for similar instruments and for small calibration sets, a portion of the original calibration used as update samples, comprising 25-33% of the original calibration selected using a Kennard-Stone design and measured on the secondary instrument, is sufficient to obtain a global calibration model with performance similar to that of the original, single-instrument calibration model [7,14,15]. The update standards need not match those used in the original calibration, but with a large calibration set, it is necessary to either have many update standards or to weight them so that the update samples contribute sufficiently to the global model [9,10].…”