Investigating the effect of flexible constraints on the accuracy of self‐modeling curve resolution methods in the presence of perturbations

Abstract

Self-modeling curve resolution methods have continuously been improved during recent years. Many efforts have been made on curve resolution methods to reduce the rotational ambiguity by means of different types of constraints. Choosing proper constraints and cost functions is critically important for the reduction of the rotational ambiguity because the constraints have a direct influence on the accuracy of the area of feasible solution (AFS). In this work, we introduce a new improved cost function, which serves to apply nonnegativity, unimodality, equality, and closure constraints. We also investigate the reduction of the AFS under hard and soft constraints. Another point of this work is to evaluate the accuracy and precision of the reduced AFS in the presence of noise and perturbations, under hard and soft implementation of nonnegativity, unimodality, equality, and closure constraints. A comparison is given between the reduced AFS with soft constraints (small deviations from constraints are accepted) and the reduced AFS under hard constraints (restrictedly forced constraints). A graphical visualization of this comparison is presented for various model problems. The resultsshow that an AFS computation with soft constraints provides more reliable results, especially in the presence of noise. The test problems substantiate significant advantages of soft constraints over hard constraints because the obtained profiles are closer to the potentially true noisy profiles, which contain small deviations from ideal responses. Using tunable parameters ", , !, ı is one of the advantages of soft constrained cost function that allows the small deviations from ideal responses. Ultimately, soft constraints can help to reduce the lack-of-fit, and they are a proper instrument to handle the effect of noise on the AFS.

Simultaneous construction of dual Borgen plots. I: The case of noise‐free data

“…This restricts these approaches to model data. Another drawback of the geometric constructions is that no approach has yet been devised for a combination with soft constraints as unimodality or monotonicity; see previous studies() for such combinations in the context of numerical optimization‐based MCR methods. Equality constraints, see other works,() can principally be integrated to the Borgen plot techniques.…”

Photoluminescence Probes in Data-Enabled Sensing

“…In most cases, a priori knowledge can be incorporated into the model in terms of various constraints to reduce the solution space of SMCR. The most widely used constraints are non-negativity, unimodality, and closure (97).…”

Closure constraint in multivariate curve resolution

“…This constraint is applied sample by sample (row by row), and it results to be a rather hard constraint since after application is fulfilled for all samples. Besides, several studies have been devoted to the investigation of the flexible constraints (eg, closure constraint) in the presence of noise and perturbations …”

“…The effect of hard modeling constraint, partial knowledge of factors, equality constraint, trilinearity constraint in the resolution of three‐way data sets, multiset data, and its effects on the range of feasible solutions have been studied by the visualization of feasible regions. Moreover, hard and soft implementation of nonnegativity, uni‐modality, and equality constraints were focused . Although closure constraint can be applied in different ways, their effects on the feasible regions were not visualized yet.…”