The calibration strategy described in this work takes advantage of the synergic combination of temperature-induced spectral variation in Near Infrared (NIR) spectroscopy and the properties of tensor models. Rather than seeing spectroscopic temperature effects as artefacts that have to be circumvented or eliminated, a Parallel Factor (PARAFAC) model is used to extract and separate the relevant sources of information about the physical and chemical changes in a system. This information is highly related to the sources that provoke changes in the system as a function of temperature, but cannot be ascribed directly to them, mainly due to the nonlinearities induced in the spectra. For quantification purposes Multiple Linear Regression (MLR) is used to build a least squares calibration model from the PARAFAC sample scores. Temperature plays a key role in our strategy by providing an additional, meaningful dimension to a standard two dimensional spectroscopic data structure, thereby turning the quantification and qualification task into a tensor problem. That way the temperature effect on the spectral data can be modelled and predicted in a straightforward and highly effective way using this novel approach. The combining strategy has been successfully applied to two NIR data sets. The first one is a laboratory off-line data set well-known, described and utilised by different research groups for testing new methods to cope with the temperature effect, treating it as an undesirable artefact. The other set is a batch process in-line data set with simultaneous changes in temperature and chemical composition. In this paper we will introduce a novel way of generating tensor data, show the advantages from an interpretational and predictive point of view, and present a comparison with traditional chemometric tools. © 2006 Elsevier B.V. All rights reserved.
Peinado, A. C., van den Berg, F., Blanco, M., & Bro, R. (2006). Temperature-induced variation for NIR tensor-based calibration. Chemometrics and Intelligent Laboratory Systems, 83(1), 75-82. https://doi.org/10.1016/j.chemolab.2006.01.006