Chemometrical study of spectral curve fitting constraint on self‐modelling curve resolution methods

Abstract

AbstractRotational ambiguity is a significant concern of chemometricians when using soft modeling methods to resolve bilinear data. Applying different types of constraints appropriate to a system under study can significantly reduce rotational ambiguity in soft models and the resulting range of feasible solutions. The first and most commonly used constraint is non‐negativity and can be applied to concentration and spectral response profiles as appropriate. Unimodality constraints, trilinearity constraints, and physical chemical modeling of concentration profiles are natural constraints that can significantly reduce rotational ambiguity in soft modeling curve resolution methods. Also, functional fitting of spectral response profiles (eg, peak shape modeling) has been used as a constraint for resolving spectroscopic data matrices. In the present work, the use of peak shape model constraints for spectral profiles was investigated using the Voigt function (a combination of Gaussian and Lorentzian functions). Mixture spectra of a simulated two‐component system and a real data set were fitted to several different Voigt models.The results of applying peak shape models on the range of feasible solutions for simulated and real data sets and simultaneously fitting the data to different models show that spectral peak shape constraints are not effective for limiting the range of feasible bands. Indeed, the non‐specific spectral Voigt model does not provide enough information about spectra to be effective for significant reduction of rotational ambiguity. These studies show that in the absence of sufficient information, many sets of peak functions can be well‐fitted to spectra and rotational ambiguity is not improved when resolving bilinear spectroscopic data.