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Ottaway J, Kalivas JH, Andries E. Spectral multivariate calibration with wavelength selection using variants of Tikhonov regularization. Appl Spectrosc. 2010;64(12):1388-95doi: 10.1366/000370210793561655.
Ottaway, J., Kalivas, J. H., & Andries, E. (2010). Spectral multivariate calibration with wavelength selection using variants of Tikhonov regularization. Applied spectroscopy, 64(12), 1388-95. https://doi.org/10.1366/000370210793561655
Ottaway, Joshua, et al. "Spectral multivariate calibration with wavelength selection using variants of Tikhonov regularization." Applied spectroscopy vol. 64,12 (2010): 1388-95. doi: https://doi.org/10.1366/000370210793561655
Ottaway J, Kalivas JH, Andries E. Spectral multivariate calibration with wavelength selection using variants of Tikhonov regularization. Appl Spectrosc. 2010 Dec;64(12):1388-95. doi: 10.1366/000370210793561655. PMID: 21144157.
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Appl Spectrosc. 2010 Dec;64(12):1388-95. doi: 10.1366/000370210793561655.

Spectral multivariate calibration with wavelength selection using variants of Tikhonov regularization.

Applied spectroscopy

Joshua Ottaway, John H Kalivas, Erik Andries

Affiliations

  1. Department of Chemistry, Idaho State University, Pocatello, Idaho 83209, USA.

PMID: 21144157 DOI: 10.1366/000370210793561655

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.

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