Sign Constraints Improve the Detection of Differences between Complex Spectral Data Sets: LC−IR As an Example

Abstract

Spectroscopy is a fast and rich analytical tool. On many occasions, spectra are acquired of two or more sets of samples that differ only slightly. These data sets then need to be compared and analyzed, but sometimes it is difficult to find the differences. We present a simple and effective method that detects and extracts new spectral features in a spectrum coming from one set with respect to spectra of another set on the basis of the fact that these new spectral features are essentially positive quantities. The proposed procedure (i) characterizes the spectra of the reference set by a component model and (ii) uses asymmetric least squares (ASLS) to find differences with respect to this component model. It should be stressed that the method only focuses on new features and does not trace relative changes of spectral features that occur in both sets of spectra. A comparison is made with the conventional ordinary least squares (OLS) approach. Both methods (OLS and ASLS) are illustrated with simulations and are tested for size-exclusion chromatography with infrared detection (SEC-IR) of mixtures of polymer standards. Both methods are able to provide information about new spectral features. It is shown that the ASLS-based procedure yields the best recovery of new features in the simulations and in the SEC-IR experiments. Band positions and band shapes of new spectral features are better retrieved with the ASLS than with the OLS method, even those which could hardly be detected visually. Depending on the spectroscopic technique used, the ASLS-based method facilitates identification of the new chemical compounds.