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Systematic comparison and potential combination between multivariate curve resolution–alternating least squares ( MCR‐ALS ) and band‐target entropy minimization ( BTEM )
Author(s) -
Bertinetto Carlo Giuseppe,
Juan Anna
Publication year - 2018
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.3000
Subject(s) - chemometrics , entropy (arrow of time) , spectral resolution , singular value , minification , mathematics , least squares function approximation , chemistry , raman spectroscopy , spectral line , algorithm , biological system , analytical chemistry (journal) , eigenvalues and eigenvectors , optics , mathematical optimization , statistics , physics , chromatography , thermodynamics , biology , quantum mechanics , astronomy , estimator
This work does a systematic comparative evaluation of 2 methods originating from different fields, both dedicated to the problem of curve resolution/unmixing: multivariate curve resolution–alternating least squares (MCR‐ALS) and band‐target entropy minimization (BTEM). The MCR‐ALS factorizes the data matrix into spectral and concentration profiles that satisfy constraints expressing physicochemical knowledge on the analyzed system. The BTEM reconstructs the pure components' spectral profiles as linear combinations of singular vectors that minimize the spectral entropy and contain specific peaks. Both methods were applied to 40 simulated and one real data set. The simulated data were generated from real spectral and concentration profiles that include different types of spectroscopy (mass spectrometry, Raman, and UV‐visible), data structures (random mixtures, images, and reaction system), and noise levels; the real data set was a Raman image of kidney calculus. For most data sets, both methods yielded accurate solutions, with a correlation between reference and resolved profiles >0.99. However, MCR‐ALS (here used with nonnegativity constraint only) was affected by rotational ambiguity in the recovery of spectral profiles coming from systems with high correlation or overlap in the concentration direction, whereas BTEM tended to distort UV‐visible spectra, a kind of measurement far in nature from low entropy conditions. MCR‐ALS solutions were more stable than BTEM to the increase in noise level. This work also explores the possibility of combining the 2 methods by performing them in sequence. The results show that this combination can significantly improve the outcome as compared to either method applied alone.