A general rule for uniqueness in self-modeling curve resolution methods

Abstract

Self-modeling curve resolution (SMCR) techniques are widely applied for resolving chemical data to the pure-component spectra and composition profiles. In most circumstances, there is a range of mathematical solutions to the curve resolution problem. The mathematical solutions generated by SMCR obey the applied constraints coming from a priori physicochemical information about the system under investigation. However, several studies demonstrate that a unique solution can be obtained by implementing some constraints such as trilinearity, equality, zero concentration region, correspondence, local-rank, and non-negativity under data-based uniqueness (DBU) condition. In this research, a general rule for uniqueness (GRU) is proposed to unify all the different information that lead to a unique solution in one framework. Moreover, GRU can be a guide for developing new constraints in SMCR to get more accurate solutions. The authors are delighted to dedicate this manuscript to Professor Paul J. Gemperline in recognition of his significant contributions to the field of chemometrics. We believe that the chemometrics society's success in addressing its mission owes a great deal to his vision, passion for learning and teaching, and extensive scientific efforts over the years. We honor his friendship and generous supports.