Investigating Soft Known-Value Constraints in Multivariate Curve Resolution Studies

In multivariate curve resolution studies (MCR), applying partial or incomplete knowledge of reference values as known-value constraints can considerably reduce the extent of rotational ambiguity. MCR under known-value constraints can be applied for both quantification and identification analysis [1]. In the presence of noise and non-ideal behavior of chemical species, MCR may not find a set of solutions that completely obey the constraints and, sometimes, the estimated solutions show severe lack of fit. In practice, limitations in the reference methods or procedures cause deviation in measured known values. In these situations, applying known values may result in considerable quantification errors in MCR results and also can challenge identification analysis. This contribution investigates the effect of applying known-value constraint on the results of MCR methods. For this purpose, a new Matlab code is written that provides the possibility of calculating the range of feasible MCR solutions under soft known-value constraints. Several simulated examples and an experimental data set were analysed using this code by providing sufficient information that theory suggests for obtaining a unique solution. The obtained ranges of feasible solutions were compared to the results of multivariate cure resolution alternating least squares (MCR-ALS) [2], and partial least squares (PLS) [3]. In the case of simulated data, an experimental design was used to evaluate the effect of two factors: (1) the amount of experimental noise, (2) and the amount of deviation of known values from true ones on the extent of rotational ambiguity.