Multivariate calibration models are sensitive to wavelength shifts in calibration spectra as such disturbances are linearly independent from unshifted spectra and increase the calibration model's dimension. However, if wavelength shifts included in the calibration model are random, the predictability of the model is not improved. On the contrary, overfitting is introduced, thereby increasing the prediction error. Because calibration spectra are defined to be error free and are the only available data at that point, there is no analytical way to find out that the calibration model is erroneous. This study gives a mathematical explanation of how the model's dimension is increased by wavelength shifts and that the additional basis vectors, principal components for instance, possess derivative-shaped features. It is also demonstrated by means of an example that the reverse is not necessarily true. Hence, derivative-shaped features found in principal components are no indication of wavelength-shifted calibration spectra. A method is presented for analyzing calibration spectra for such shifts. The algorithm takes advantage of the fact that artificial shift compensations of true shifts increase the similarity, i.e., correlation, of shifted spectra with respect to the remaining, unshifted spectra. Synthetic and experimental data are used to demonstrate and assess the performance of the algorithm. It is shown that wavelength shifts in calibration spectra can be detected and corrected if a small number of spectra are disturbed. Significant improvements of the prediction errors of chemometric calibration models can be achieved by means of this shift-correction algorithm.
Arizona State University, Department of Chemistry and Biochemistry, Mail stop 1604, Tempe, Arizona 85287
Publication date: May 1, 2004
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The Society publishes the internationally recognized, peer reviewed journal, Applied Spectroscopy, which is available both in print and online. Subscriptions are included with membership or can be purchased by institutional or corporate organizations. Abstracts may be viewed free of charge. Previously published as Bulletin (Society for Applied Spectroscopy)