Investigation of the equality constraint effect on the reduction of the rotational ambiguity in three-component system using a novel grid search method

• Studying the effect of the equality constraint on the rotational ambiguity.
• Extending grid search method using SPSO to find solutions are corresponding.
• The equality constraint effect on complementary space shown by linear algebra.

The obtained results by soft modeling multivariate curve resolution methods often are not unique and are questionable because of rotational ambiguity. It means a range of feasible solutions equally fit experimental data and fulfill the constraints. Regarding to chemometric literature, a survey of useful constraints for the reduction of the rotational ambiguity is a big challenge for chemometrician. It is worth to study the effects of applying constraints on the reduction of rotational ambiguity, since it can help us to choose the useful constraints in order to impose in multivariate curve resolution methods for analyzing data sets. In this work, we have investigated the effect of equality constraint on decreasing of the rotational ambiguity. For calculation of all feasible solutions corresponding with known spectrum, a novel systematic grid search method based on Species-based Particle Swarm Optimization is proposed in a three-component system.

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