Predicting the uniqueness of single non-negative profiles estimated by multivariate curve resolution methods

In many kinds of chemical data, one or more species are unknown and the only efficient way to identify and/or quantify them is by mathematical resolution of the mixture spectra. The major problem with such mathematical decompositions is the possibility of obtaining a range of feasible solutions instead of a unique solution due to insufficient prior information about the system under study. However, even with the minimal non-negativity assumptions, there may be some levels of uniqueness, i.e., full/partial/fractional, in the results of the bilinear decomposition of chemical data which is very important to detect. In this study, a procedure is proposed to predict the uniqueness of the resolved non-negative profiles obtained by MCR-ALS (or analogous methods like NMF, EFA, SIMPLISMA, ITTFA, HELP, etc.). This uniqueness prediction is based on the data-based uniqueness (DBU) theorem and the general rule of uniqueness (GRU) presented in previous studies. The proposed procedure is easy to implement, has no additional computational cost, and is general for different systems with any number of components. Several simulated and experimental datasets containing different numbers of components were used to examine and evaluate the proposed procedure.