A new ingenious combination of rank annihilation factor analysis (RAFA) and self-modeling to enhance the unambiguous resolution of multicomponent spectra

Abstract

In the article, a novel chemometric method for resolution of three-component spectral mixtures is presented and thoroughly scrutinized. Its main core is based on the concept of 'soft' data self-modeling using the SVD factorization (SVD-SM). Each spectrum is then represented as an element of the geometric object known as a simplex which, in this case, takes a form of a triangle. Since its vertices are defined by the spectra of the mixture's pure components, the carried out analysis comes down to a proper determination of the vertices locations. As opposed to the conception of doing so by estimating the areas of feasible solutions (AFS), the idea of unambiguous identification of the simplex's sides is introduced. This may be achieved through a neat application of the rank annihilation factor analysis (RAFA), which allows for generation of two-component difference spectra, whose point representations mark the edges of the searched triangle. Consequently, the obtained final results remain highly unique. In the paper, basics and details of the outlined hybrid RAFA-SVD-SM method are critically discussed from both conceptual and practical points of view. Finally, effectiveness of the proposed algorithm (written in MATLAB) is (successfully) validated on a few series of experimental quenched fluorescence spectra. The high enough recovery rate of the individual component spectra qualifies the proposed approach to be a justifiable alternative for the several well-established chemometric methods tested in the study, including GRAM and PARAFAC.

Keywords: Factor Analysis; Fluorescence Quenching; Rank Annihilation; Resolution of Multi-Component Spectra; Self-modeling; Spectral Mixtures.