Evolutionary Factor Analysis

Abstract

Because of chemical interconversion, many chemical systems cannot be physically separated, making chemical identification and quantification difficult. The spectra (IR, UV, Visible, Raman, CD, etc.) of such systems exhibit overlapping contributions of uncataloged components, confounding the identification as well as the quantification. Strategies based on factor analysis [1], a chemometric technique for handling complex multi-dimensional problems, are ideally suited to such problems. Abstract factor analysis (AFA) reveals the number of spectroscopically visible components. Evolutionary factor analysis (EFA) [2-4] takes advantage of experimental variables that control the evolution of components, revealing not only the concentration profiles of the components but also their spectra even when there are no unique concentrations or spectral regions. Evolutionary factor analysis makes use of the fact that each species has a single, unique maximum in its evolutionary concentration distribution curve. We have recently applied this self-modeling method to the infrared spectra of stearyl alcohol in carbon tetrachloride solution. The evolutionary process of this system was achieved by increasing the concentration of stearyl alcohol from 0.0090 to 0.0800 g/L in 15 stages, each time recording the IR spectra from 3206 to 3826 cm '. The spectra were corrected for baseline shift, solvent absorption and reflectance losses. The 15 spectra were then digitized every 3 cm ' and assembled into a 35 x 15 absorbance matrix [A] appropriate for factor analysis. The factor indicator function [1], the reduced eigenvalue [5] and cross validation [6] indicated that three species contribute to the observed spectra. Thus AFA expresses the data matrix as a product of a 35 x 3 absorptivity matrix [E],,,, and 3 X 15 abstract concentration matrix [C],h,,.