Use of spherical projections in factor analysis of mid-infrared spectra of mixtures

Abstract

Previously, window factor analysis has been applied to mid-infrared spectra of mixtures. A difficulty encountered is identifying regions of the mixture spectra where only one compound absorbs (‘composition one’ regions). This paper presents an alternative to the conventional method of using eigenvalues. For three-component mixtures, three principal components (PCs) are calculated, the data is normalized to lie on the surface of a sphere and a spherical projection is calculated. In the absence of noise, composition one regions lie on the corners of a triangle on the surface of the sphere. The method is applied to both simulated and real data, and the effect of noise is demonstrated.