Calculation and Meaning of Feasible Band Boundaries in Multivariate Curve Resolution of a Two-Component System

Results obtained by model-free multivariate curve resolution (MCR) methods often are complicated by rotational and scale ambiguities, meaning that a range of feasible solutions describing and fitting experimental data equally well and fulfilling the constraints of the system are possible. In this work, two recent proposals to examine this problem and their relation are compared and discussed for the case of a two-component system. In one of these approaches, a systematic grid search of all feasible solutions is performed, and the results are displayed in appropriate mesh and contour plots which reveal their boundaries. In a second approach, an objective function is defined in terms of the relative signal contribution of every chemical species, and this function is maximized and minimized to get its extreme values that satisfy the constraints. These extreme values can also be represented graphically in the previously obtained mesh and contour plots. It turns out that the results obtained by these two approaches are in agreement and that the same extreme values are identified as boundaries of the band of feasible solutions, proving their reliability and their possible general application for the validation of MCR results.