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.
引用
Alejandro Olivieri (2024). N-BANDS: toolbox for estimating rotational ambiguity (https://www.mathworks.com/matlabcentral/fileexchange/134501-n-bands-toolbox-for-estimating-rotational-ambiguity), MATLAB Central File Exchange.
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Olivieri, Alejandro C., and Romà Tauler. “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.” Journal of Chemometrics, vol. 35, no. 3, Wiley, Nov. 2020, doi:10.1002/cem.3317.
Olivieri, Alejandro C., and Romà Tauler. “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.” Journal of Chemometrics, vol. 35, no. 3, Wiley, Nov. 2020, doi:10.1002/cem.3317.
APA
Olivieri, A. C., & Tauler, R. (2020). 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. Journal of Chemometrics, 35(3). Wiley. Retrieved from https://doi.org/10.1002%2Fcem.3317
BibTeX
@article{Olivieri_2020,
doi = {10.1002/cem.3317},
url = {https://doi.org/10.1002%2Fcem.3317},
year = 2020,
month = {nov},
publisher = {Wiley},
volume = {35},
number = {3},
author = {Alejandro C. Olivieri and Rom{\`{a}} Tauler},
title = {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},
journal = {Journal of Chemometrics}
}
Olivieri, Alejandro C. “Estimating the Boundaries of the Feasible Profiles in the Bilinear Decomposition of Multi-Component Data Matrices.” Chemometrics and Intelligent Laboratory Systems, vol. 216, Elsevier BV, Sept. 2021, p. 104387, doi:10.1016/j.chemolab.2021.104387.
Olivieri, Alejandro C. “Estimating the Boundaries of the Feasible Profiles in the Bilinear Decomposition of Multi-Component Data Matrices.” Chemometrics and Intelligent Laboratory Systems, vol. 216, Elsevier BV, Sept. 2021, p. 104387, doi:10.1016/j.chemolab.2021.104387.
APA
Olivieri, A. C. (2021). Estimating the boundaries of the feasible profiles in the bilinear decomposition of multi-component data matrices. Chemometrics and Intelligent Laboratory Systems, 216, 104387. Elsevier BV. Retrieved from https://doi.org/10.1016%2Fj.chemolab.2021.104387
BibTeX
@article{Olivieri_2021,
doi = {10.1016/j.chemolab.2021.104387},
url = {https://doi.org/10.1016%2Fj.chemolab.2021.104387},
year = 2021,
month = {sep},
publisher = {Elsevier {BV}},
volume = {216},
pages = {104387},
author = {Alejandro C. Olivieri},
title = {Estimating the boundaries of the feasible profiles in the bilinear decomposition of multi-component data matrices},
journal = {Chemometrics and Intelligent Laboratory Systems}
}