Noise propagation and error estimations in multivariate curve resolution alternating least squares using resampling methods

Abstract

Different approaches for the calculation of prediction intervals of estimations obtained in multivariate curve resolution using alternating least squares optimization methods are explored and compared. These methods include Monte Carlo simulations, noise addition and jackknife resampling. Obtained results allow a preliminary investigation of noise effects and error propagation on resolved profiles and on parameters estimated from them. The effect of noise on rotational ambiguities frequently found in curve resolution methods is discussed. This preliminary study is shown for the resolution of a three-component equilibrium system with overlapping concentration and spectral profiles.

Characterization and prediction of solute properties in methanol–water association by chemometrics analysis of solvation data

“…Some methods [15] such as real error (RE), imbedded error, x function and indicator function are available that can estimate the correct number of factors in a system. MCR analysis [16,[19][20][21][22][23][24] is a class of chemometrics techniques that are concerned with the resolving of concentration profile and pure responses of the species present in given chemical equilibrium. These techniques are routinely applied to the spectroscopic and electrochemical data to investigate the complex chemical reactions.…”

ICE: a new method for the multivariate curve resolution of hyperspectral images

“…Finally, in contrast to the methods of Gemperline [35] or Tauler and co-workers [36,37] that obtain feasible bands for the endmember spectra, the ICE algorithm currently does not provide error bounds on the estimated proportions, nor on the estimated endmembers, but this too is an area of current research. It may be that a hierarchical model which includes a spatial model for the proportions provides a way forwards.…”

Quality assessment of the results obtained by multivariate curve resolution analysis of multiple runs of gasoline blending processes

“…Improved conditions for better species resolution may be achieved when multiple experiments are analyzed together instead of one by one, particularly in situations of rank-deficiency [4]. Despite of the increasing popularity of MCR-ALS, few studies have been done until now to investigate the reliability of the solutions (concentration and spectra profiles) estimated using this approach [5][6][7].…”

“…In order to obtain error estimations and confidence limits for the solutions obtained by non-linear optimization methods, resampling methods have been proposed [17][18][19][20]. In a previous work [6], some resampling approaches were tested for MCR-ALS. The noise addition resampling method was considered to be the more suitable because of the quality of the obtained results and the little need of computational resources and time of analysis.…”