Curve resolution, ambiguous

R. Tauler, A.K. Smilde and B.R. Kowalski, Selectivity, local rank, three-way data analysis and ambiguity in multivariate curve resolution. J. Chemom., 9 (1995) 31-58. 

Depending on the quality of data and the method selected, constraints on the parameters to be estimated may be required in order to get a chemically meaningful solution. In the case of multivariate curve resolution (MCR) (see Section 3.2) performed on one 2D NMR spectrum, application of constraints is mandatory. If constraints are not applied, it can be shown that there is an infinity of equally well-fitting solutions and hence the true underlying parameters (spectra, concentrations) cannot be estimated directly. This is known as the rotational ambiguity of two-way low-rank models. 

Depending on the situation, there are several unknowns in Equation (10.4). In its most general case the unknowns are a, a2, bi, b2, c2ji and c2j2. The standard Xi has pseudorank one (see Chapter 2, Section 6), and, hence, can be decomposed in its contributions ai and bi. Note that there is still intensity ambiguity because aibl equals aiQ Q 1b y, for any nonzero a. The quantification of the analyte requires the estimation c2,i and sometimes it is also convenient to obtain estimates of ai, a2, bi and b2 for diagnostics purposes. This is the curve resolution aspect of second-order calibration. 

The concept of ambiguity in curve resolution is linked to the fact that a range of CS products can reproduce the original data set with the same optimal fit. 

Jaumot, J. and Tauler, R. (2010). MCR-BANDS A user friendly MATLAB program for the evaluation of rotation ambiguities in multivariate curve resolution. Chemometr. Intell. Lab. Syst., 103, 96-107. 

Detector saturation can effect both quantitative and qualitative data analysis, and each of these effects should be appreciated. The effect on sample quanti-tation is intuitive, where for instance a twofold increase in sample concentration produces a less than twofold increase in response. This will cause a flattening of calibration curves at higher concentrations. For API techniques, source saturation (or ion suppression) is another source of response saturation independent of detector saturation. Detector saturation can also effect qualitative measurements such as mass accuracy and isotope ratio calculations. In the former, when a mass spectral peak that has some finite resolution stalls to saturate the detector the peak-top calculations that provide the m/ measurement of the peak will become ambiguous. Likewise, it is possible that as one isotope of an ion starts to saturate the detector, adjacent isotopes in the distribution will still provide a linear response. The result of this is that incorrect isotope ratios will be obtained. Changes in relative isotope ratios of individual spectra across a chromatographic peak is an indicator of possible detector saturation. 

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