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

Abstract

A new algorithm named N-BANDS has been developed for the estimation of the combined effect of noise and rotational ambiguity in the bilinear decomposition of data matrices using the popular multivariate curve resolution–alternating least-squares model. It is based on a nonlinear maximization and minimization of a component-wise signal contribution function (SCF), with a single-objective function and a separate module for applying a variety of constraints. The algorithm can be applied to multicomponent systems and efficiently estimates the extreme component profiles corresponding to maximum and minimum SCF in the presence of varying amounts of instrumental noise. Simulated systems mimicking multicomponent and multisample analytical calibration protocols have been studied, having uncalibrated interferents in the test samples. Different noise structures (independent and identically distributed, proportional and correlated) were added to the data matrices, with results that indicate an increase in the extension of feasible bands as the noise level increases.