Two-Way Data Analysis: Multivariate Curve Resolution – Iterative Resolution Methods

This chapter describes the general modus operandi of model-free multivariate curve resolution (MCR) iterative methods, that is, the recovery of pure concentration profiles and responses (spectra) from the iterative optimization of initial estimates under the action of constraints. Initially, some common concepts, such as methodologies for the generation of initial estimates or the description of the most common constraints, are presented. The basic bilinear curve resolution (CR) model is expressed in two different forms: X = CST + E or X = (CoR)(R−1SoT) + E. Methods based on the first equation solve for the C and/or ST matrices directly, whereas methods based on the second equation optimize the transformation matrix R in such a way that C = CoR and ST = R−1SoT are chemically meaningful. Resolving factor analysis (RFA) and the resolution of matrices through elementary matrix transformations (Gentle) are selected as algorithms representative of the optimization via transformation matrices and are described in detail in this chapter. The most representative methods based on the direct, iterative solution for C and ST that are described in this chapter are iterative target transformation factor analysis (ITTFA) and multivariate curve resolution-alternating least squares (MCR-ALS). Critical comments and graphical examples of the use and the applicability of the different methods are also included.

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