LAUSR

Abstract The results by soft modeling multivariate curve resolution methods often are not unique and are questionable because of the rotational ambiguity. It means a range of feasible solutions equally fits experimental data and fulfills the constraints. Regarding to chemometric literature, the reduction of the rotational ambiguity in multivariate curve resolution problems is a major challenge in order to construct effective chemometric methods. It is worth to study the effects of applying constraints on the reduction of the rotational ambiguity, since it can help us to choose the useful constraints for multivariate curve resolution methods for analyzing data sets. The aim of this work is to demonstrate the impact of monotonicity and unimodality constraints on the full set of all feasible, nonnegative solutions. We compared the results of two constraints in different two- and three-component systems. To reach this goal, two simulated kinetic and equilibrium data sets are used. Moreover, an experimental data set related to a mixture of two uniprotic acid solutions at different pH values as a model for equilibrium systems is used to extend the discussions to real cases. It is shown in this work that monotonicity is a meaningful chemistry-based constraint which in some cases is more effective than unimodality.