Systematic comparison and potential combination between multivariate curve resolution–alternating least squares (MCR‐ALS) and band‐target entropy minimization (BTEM)

Abstract

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.

Operandomonitoring of mechanisms and deactivation of molecular catalysts

“…For each BT, the algorithm finds a linear combination of the selected vectors that satisfy minimum entropy, and non-negativity of the spectra. 99 BTEM has the additional advantage of not requiring initial estimates of the number of species present, which helps the elucidation of complex reaction mechanisms. 21,105 Recently, a comparison between MCR-ALS and BTEM was published, where the authors implement the use of these techniques separately and jointly to mass and UV-Vis spectra as well as Raman images.…”

“…On the other hand, BTEM led to more accurate profiles in Raman and mass spectra data sets as well as being better at reducing the rotational ambiguity of data. 99 BTEM had previously been compared to MCR techniques to obtain the pure The user must select a pure wavelength and an average spectrum is calculated from the mixture spectra. The difference between the average and each of the mixture spectra determines a standard deviation.…”

A multivariate curve resolution analysis of multicenter proton spectroscopic imaging of the prostate for cancer localization and assessment of aggressiveness

“…in which C is the matrix of the relative intensity of the profiles, S T is the transposed matrix of pure spectral profiles of identified components, and E is the matrix of residuals not explained by the resolved components. 28 Using the number of valuable components outcome of the SVD operation, the initial C or S T estimates were determined by band-target entropy minimization. Then, the estimated profiles are iteratively optimized by calculating one matrix, either C or S T from Equation (1), setting constraints.…”

“…A well-established PR approach is multivariate curve resolution (MCR), which processes spectroscopic data employing a mixture of underlying spectral components. 28 MCR encompasses a wide range of algorithms that decompose these data by expressing them in a bilinear model with relevant contributions of pure components. The process involves a data-driven factorization of the initial data matrix into the product of two matrices containing the pure response profiles of the different components in the data and their relative amounts.…”

“…The process involves a data-driven factorization of the initial data matrix into the product of two matrices containing the pure response profiles of the different components in the data and their relative amounts. [28][29][30] Consequently, MCR provides component profiles that represent the natural properties expected from the spectroscopic data, such as combinations of metabolite signals specific for normal prostate tissue or tumor lesions. It is well suited for automated spectroscopic evaluation of all voxels in an MRSI data matrix of the prostate.…”