2010
DOI: 10.1002/cem.1273
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Pure component spectral recovery and constrained matrix factorizations: concepts and applications

Abstract: We present new ideas underlying a self-modelling factor analytical method which allows to extract pure component spectra and the associated concentration profiles from a set of spectroscopic measurements. The usefulness of the method is demonstrated and compared with established tools for model problems and for a system from catalytic hydroformylation by Rhodium complexes both with overlapping component spectra. Self-modelling methods tend to minimize the overlap of the recovered spectra, which can result in a… Show more

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Cited by 46 publications
(47 citation statements)
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“…27,28 In this regard, the data analysis combines classical MCR techniques with the relatively new complementarity theory. 31 The concentration proles are similar for all studied dyes. In all cases two of the three pure component spectra are available.…”
Section: Pure Contribution Of Species and Stoichiometric Analysismentioning
confidence: 76%
See 1 more Smart Citation
“…27,28 In this regard, the data analysis combines classical MCR techniques with the relatively new complementarity theory. 31 The concentration proles are similar for all studied dyes. In all cases two of the three pure component spectra are available.…”
Section: Pure Contribution Of Species and Stoichiometric Analysismentioning
confidence: 76%
“…[31][32][33] Whenever additional information on the pure component factors is available, it should be used in order to reduce the rotational ambiguity; see e.g. The number of signicant singular values indicates the number of independent components.…”
Section: Data Analysis Methodsmentioning
confidence: 99%
“…The pure component spectra of these species and the associated concentration profiles were extracted with an algorithm based on factor analysis. [38] Their relative concentrations during the reaction are shown in Figure 11.…”
Section: A C H T U N G T R E N N U N G Ammonium Hydrogen Undecacarbonmentioning
confidence: 99%
“…(2) The rows of A are scaled so that the coefficients of the linear combinations of each row of A with respect to the first right singular vector of D equals 1. For the singular value decomposition [16] of the spectroscopic data matrix D see [18] and Section 2.2. Theorem 2.2 in [9] proves that this coefficient is nonzero under a certain weak assumption on D. In the following, we call this f irst right singular vector scaling the FSV-scaling.…”
Section: The Row Sum Scaling and The First Singular Vector Scalingmentioning
confidence: 99%