Analytical solution for determining feasible regions of self‐modeling curve resolution (SMCR) method based on computational geometry

Abstract

AbstractDuring 20 years the analytical solution for determining feasible regions of self‐modeling curve resolution (SMCR) method was only slightly researched. After publishing of the famous papers of Borgen et al. in 1985 and 1986, pure generalizations have not been given and even investigated. The reason might have been that the published algorithms and descriptions have been hard to interpret (to code) and to understand respectively. In this paper, several theoretical reasoning is revised giving clearer and more general proofs for principles of SMCR, that is the normalized responses are embraced in the (N−1)‐dimensional simplex with the vertices being the N‐normalized pure profiles. For the first time in the chemometric literature, computational geometry tools are introduced instead of, for example, linear programming tools, for developing our algorithm to draw Borgen plots of any three‐component systems. Numbers of illustrations are given for the sake of clarity. As it has turned out, the highly cited and used data matrix published by Lawton and Sylwestre has not two but more components as it is presented in detail. For a simulated three‐component system, Borgen plots are drawn and some explanations are given. Copyright © 2006 John Wiley & Sons, Ltd.