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Non‐negativity constraints for elimination of multiple solutions in fitting of multivariate kinetic models to spectroscopic data
Author(s) -
Jaumot Joaquim,
Gemperline Paul J.,
Stang Alexandra
Publication year - 2005
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.914
Subject(s) - maxima and minima , univariate , multivariate statistics , kinetic energy , least squares function approximation , mathematics , data point , ambiguity , curve fitting , computer science , algorithm , statistics , physics , mathematical analysis , quantum mechanics , estimator , programming language
Multiple solutions arise when fitting complicated multi‐step kinetic models to spectroscopic data. For consecutive reactions of the type A→B→C this well‐known ambiguity is due to the presence of multiple equivalent global minima in the response surfaces associated with the non‐linear least squares fitting of rate constants to spectroscopic data. Several methods have been described to overcome the ambiguity when fitting consecutive reactions with univariate data but few attempts to solve the problem have been described for multivariate data. Additionally, for complicated multi‐step reaction schemes there may be several local minima that make selection of the initial parameter guesses difficult. This paper reports a general approach to overcome these types of ambiguities in multivariate kinetic fitting methods using non‐negativity constraints for the determination of the pure component spectra estimated during the model‐fitting process. Under many conditions these constraints reduce or eliminate entirely the incorrect local minima. The effectiveness and reliability of the new constraints were tested with several simulated and real data sets. Copyright © 2005 John Wiley & Sons, Ltd.