How we can measure the uncertainties associated to Multivariate Curve Resolution solutions due to the combined effect of rotation ambiguities and experimental errors?
Multivariate Curve Resolution (MCR) methods are used for the analysis of unknown chemical mixture systems. Since Multivariate Curve Resolution (MCR) methods1 are based on the application of a bilinear model, their solutions are affected by rotation ambiguities, which means that solutions are not unique, and a range of feasible solutions can explain (fit) the observed data equally well, fulfilling the same set of constraints. Decreasing the extent of rotation ambiguities on MCR solutions can be achieved by the application of constraints in alternating least squares optimization (MCR-ALS) algorithms2. For the evaluation of the extension of rotation ambiguities associated to a particular MCR solution, the MCR-BANDS3 has been proposed based on the maximization and minimization of an objective signal contribution function (SCF) for every component of the mixture. On the other side, experimental errors and noise are propagated to the MCR solutions increasing their uncertainty. In absence of rotation ambiguities, the confidence intervals in the MCR solutions due experimental errors can be evaluated4. The study of the combined effects of these two uncertainty sources, rotation ambiguity and experimental errors, has been also attempted5. Recently the N-BANDS6 method has been proposed as an extension of the MCR-BANDS method which allows for the estimation of the uncertainties in the calculation of the MCR solutions due to the combined effects of rotation ambiguities and experimental noise.
1. Multivariate curve resolution applied to second order data, R. Tauler, Chemolab, 1995, 30, 133-146; 18.
2. Validation of alternating least squares multivariate curve resolution for chromatographic resolution and quantitation. R.Gargallo, F.Cuesta-Sànchez, D.L. Massart and R.Tauler. TRAC, 1996, 15, 279-286
3. MCR-BANDS: An user friendly MATLAB program for the evaluation of rotational ambiguity in Multivariate Curve Resolution J.Jaumot and R.Tauler. Chemolab, 2010, 103, 96–107
4. Interval estimation in multivariate curve resolution by exploiting the principles of error propagation in linear least squares. A.Mani-Varnosfaderani, E.S.Park, R.Tauler. Chemolab 206 (2020) 104166
5. Error propagation along the different regions of multivariate curve resolution feasible solutions. M.Dadashi, H.Abdollahi, R.Tauler. Chemolab, 2017, 162, 203-213
6. N-BANDS: A new algorithm for estimating the extension of feasible bands in multivariate curve resolution of multicomponent systems in the presence of noise and rotational ambiguity. A.C. Olivieri and R.Tauler. J. of Chemometrics. 2020;e3317
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