N-BANDS: toolbox for estimating rotational ambiguity

The toolbox implements N-BANDS for bilinear feasible profiles and sensor-wise N-BANDS for band boundaries in bilinear decomposition.

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 andminimization 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.

The boundaries of the range of feasible profiles in the bilinear decomposition of a data matrix are estimated by sensor-wise N-BANDS, incorporated in the toolbos. Instead of maximizing and minimizing the profile norms, sensor-wise N-BANDS approach calculates the profiles showing extreme values of the elements at each sensor in both data modes. This produces two sets of profiles for each sensor, whose envelops define the boundaries of the range of feasible solutions: the upper envelop for maximum element values represents the upper boundary, and the lower envelop the lower boundary.

Several codes are provided for implementation of both N-BANDS and sensor-wise N-BANDS.