Implementing minimum entropy constraint in MCR-ALS

Carlo Bertinetto, Iina Solala, Anna De Juan

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Multivariate Curve Resolution – Alternating Least Squares (MCR-ALS) [1] is a curve resolution method based on factorizing the data matrix into spectral and concentration profiles under constraints. The aim of this work is implementing and assessing a new constraint to minimize spectral entropy (which is equivalent to searching for the simplest spectra) inspired on the Band-Target Entropy Minimization (BTEM) method [2]. A previous study [3] has shown that entropy minimization can improve MCR-ALS results for signals with narrow spectral features, such as vibrational or mass spectra, when little knowledge on the profiles to be resolved, e.g. only non-negativity, is available.
The new constraint is applied by combining the spectral profiles obtained in each iterative cycle of the MCR-ALS algorithm in order to satisfy certain minimum entropy criteria. Several options are explored in the formulation of the combined algorithm: type of optimizer, type of objective function, stop criterion and sequence of application relative to the other constraints. Simulated data sets made by combining real Raman or mass spectra with concentration profiles from a real pharmaceutical image or from a first order reaction were used for this purpose. The best results were obtained in the following conditions: a) using a particle swarm optimizer in the first iteration and a Nelder-Mead simplex for the subsequent ones, b) differentiating the solutions using band targets (i.e. imposing that the solution contains a certain peak) selected by a SIMPLISMA-based method, c) including a non-negativity condition during entropy minimization and d) adding a stop criterion based on similarity among the spectral profiles of consecutive iterations. The sequence of application of the entropy constraint, which was placed either at the very beginning or right after non-negativity, did not have a clear effect on the results.
The proposed algorithm was also assessed on real Raman and IR data. In several cases the inclusion of the entropy constraint brought about a significant improvement as compared to using only non-negativity (see Fig 1), without requiring any additional knowledge on the concentration profiles.

[1] de Juan A.; Jaumot J.; Tauler R. Multivariate Curve Resolution (MCR). Solving the mixture analysis problem. Anal. Methods 2014, 6, 4964-4976.
[2] Widjaja E.; Li C.; Chew W.; Garland M. Band-target entropy minimization. A robust algorithm for pure component spectral recovery. Application to complex randomized mixtures of six components. Anal. Chem. 2003, 75, 4499-4507.
[3] Bertinetto C. G.; de Juan A. Systematic Comparison and Potential Combination between Multivariate Curve Resolution - Alternating Least Squares (MCR-ALS) and Band-Target Entropy Minimization (BTEM). J. Chemom., submitted.
Original languageEnglish
Publication statusPublished - 2017
EventScandinavian Symposium on Chemometrics - Naantali Spa, Naantali, Finland
Duration: 19 Jun 201722 Jun 2017
Conference number: 15


ConferenceScandinavian Symposium on Chemometrics
Abbreviated titleSSC
Internet address

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