Double Regularization for Temperature Correction with Tikhonov Regularization. Application to Calibration Transfer

H.C. GOICOECHEA; G.G. SIANO; E. ANDRIES; J.H. KALIVAS

Montpellier, Francia

Congreso; 11th International Conference on Chemometrics for Analytical Chemistry (CAC2008); 2008

SupAgro, Montpellier, Francia

Qualities of an analyte, such as species concentration, can be quantitatively determined using predictive multivariate calibration models. Among a number of different methods it can be found Tikhonov regularization (TR) [2] which is an approach to form a multivariate calibration model for y = Xb. It includes a regulation operator matrix L which can be used to remove unwanted spectral artifacts. In this way a regression vector is sought that can correct for irrelevant spectral variation in predicting y. In this study near-infrared (NIR) spectra measured at different temperatures, which have been studied by several other investigators [5,7], were considered. Because IR spectroscopic absorption depends on vibrational modes of molecules and these modes are affected by forces such as hydrogen bonding, which in turn are affected by temperature, these spectra act as temperature-sensitive data, which was useful for studying calibration transfer between two temperatures.  TR can be used as a calibration transfer method for correcting temperature effects. For doing that, spectra are placed in the rows of L that characterize the spectral artifacts that need to be corrected. Another option can be to place in L difference spectra of the same samples measured under different temperatures. For example, NIR spectra from calibration samples at 30ºC can be processed with TR to build a model that can predict samples at 50ºC. Matrix L in TR can be made using information from just a few spectra at 50ºC. Two approaches are considered here. One uses spectra measured at 30ºC and 50ºC without needing analyte concentration and the second only uses spectra at 50ºC but needing analyte concentration. When L itself is nearly singular, then problems arise when matrix inversions are needed in the TR algorithm. A modification was developed so that the inversion operation is stabilized. In this way, models are built and each one depends on two meta-parameters values, λ and τ. Finally, it is necessary a strategy for selecting an optimal model.