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[Display omitted] • Directions to evaluate the ambiguity in MCR-ALS solutions are given. • The impact of ambiguity on prediction uncertainty is assessed. • The effect of different constraints is shown on the ambiguity extent. • Recommendations are given to report uncertainties in MCR-ALS protocols. The aims of the present tutorial are the following: (1) to show the importance of applying all the chemically sensible constraints which are necessary to retrieve interpretable component profiles when processing second-order analytical data with multivariate curve resolution – alternating least-squares (MCR-ALS), (2) to demonstrate that the constraints allow one to reduce or even remove the impact of the rotational ambiguity in the MCR-ALS solutions, and (3) to provide details on how to estimate the uncertainty in the predicted analyte concentrations which is derived from any remaining ambiguity with a recently developed N-BANDS method. Both simulated and experimental data sets are examined for this purpose. Recommendations are given for including the ambiguity uncertainty in addition to the statistical reports and analytical figures of merit in every MCR-ALS calibration protocol, to assess the reliability of the analytical results. [ABSTRACT FROM AUTHOR]

• Multiset data analysis can be a proper way to increase the accuracy of multivariate curve resolution (MCR) results, which is dropped due to rotational ambiguity. • Unique resolution of the data can only be obtained under uniqueness conditions, i.e. resolution theorems and databased-uniqueness. However, the conditions for obtaining the unique solution by resolution theorems are entirely dependent on the estimation of selectivity and local rank information. • With multiset analysis, there is a possibility to design the calibration data sets that provide conditions for resolution theorems through the application of correspondence constraint. • Simultaneous analysis of multiple data sets, even without applying correspondence, can improve the accuracy of results and in some cases obtain the unique solution based on databased-uniqueness. Multiset data analysis can be a proper way to increase the accuracy of multivariate curve resolution (MCR) results, which is dropped due to rotational ambiguity. Resolution theorems and databased-uniqueness introduce the conditions for obtaining the unique solutions. However, the conditions for resolution theorems are dependent on the estimation of local rank information. With multiset analysis, there is a possibility to design the calibration data sets that provide conditions for resolution theorems. Therefore, correspondence constraint, which express the presence or absence of the components in each data set, can be applied in simultaneous analysis to implement the local rank information. Furthermore, simultaneous analysis even without applying correspondence can improve the accuracy of results and in some cases obtain the unique solution based on databased-uniqueness. The results can be explained by the duality concept, which explains the relationship between row and column vector spaces. Two simulated examples and one real excitation-emission fluorescence data were analyzed to explore the unique solutions. The results illustrate how a proper design of multiset data can lead to a unique solution in MCR methods while providing further information about the system. Therefore, not only multiset analysis can improve the results in well-designed data sets, but also can provide the situation to apply correspondence and lead to a unique resolution. [ABSTRACT FROM AUTHOR]