Closure constraint in multivariate curve resolution

Omidikia, Nematollah; Beyramysoltan, Samira; Jafari, Jamile Mohammad; Tavakkoli, Elnaz; Lakeh, Mahsa Akbari; Alinaghi, Masoumeh; Ghaffari, Mahdiyeh; Karimvand, Somaiyeh Khodadadi; Rajkó, Róbert; Abdollahi, Hamid

doi:10.1002/cem.2975

Cited by 17 publications

(10 citation statements)

References 33 publications

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“…To solve Equation 1, a number of components and initial estimates of either C or S T should be proposed and an iterative optimization using an alternating least squares (ALS) algorithm is performed to estimate the concentration (in C), and spectra (in S T ) profiles of the constituents (components) which better describe the analyzed data matrix, D. During the ALS optimization, different constraints like non-negativity, unimodality, closure, or local rank and selectivity can be applied to decrease the rotation ambiguities associated to the bilinear model and facilitate the convergence to chemically meaningful solutions. See references [19,21,24,35] for more details of the MCR-ALS procedure.…”

Section: Theory and Backgroundmentioning

confidence: 99%

“…In previous works in which MCR-ALS was applied to second-order data for quantitative analysis, a post-processing calibration step was performed [35]. In the postprocessing calibration step first, the peak areas or heights of the resolved concentration profiles of the analytes in the calibration samples were regressed against their known analyte concentrations.…”

Section: Theory and Backgroundmentioning

confidence: 99%

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Application of the area correlation constraint in the MCR-ALS quantitative analysis of complex mixture samples

Bayat

Marín-García

Ghasemi

et al. 2020

Analytica Chimica Acta

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The application of the recently developed area correlation constraint in Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) for the quantitative determination of analyte mixtures is shown. The feasibility of the proposed constraint is tested firstly for the calibration and quantitation of PAHs mixtures in their synthetic mixtures (validation samples) and in river water samples dissolved organic matter (DOM) using EEM fluorescent three-way data. In this case, MCR-ALS results obtained with the proposed area correlation constraint are comparable with the results obtained with methods based on the fulfillment of the trilinear model, like PARAFAC and MCR-ALS with the trilinearity constraint. Secondly, the possibility of applying this new area correlation constraint is extended to the analytical determination of lipid mixtures in synthetic and cell culture samples by LC-MS, where the trilinear model does not hold.The applicability of the proposed area correlation constraint is assessed, and it is proposed as a general tool for the quantitative determination of unknown mixtures of analytes in complex natural samples with severe profile overlapping and unknown composition, whatever the data structure is.

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Section: Theory and Backgroundmentioning

confidence: 99%

Section: Theory and Backgroundmentioning

confidence: 99%

Application of the area correlation constraint in the MCR-ALS quantitative analysis of complex mixture samples

Bayat

Marín-García

Ghasemi

et al. 2020

Analytica Chimica Acta

View full text Add to dashboard Cite

show abstract

“…Besides, the closure constraint could not be applied: it acts as a mass balance and implies that the sum of the modelled concentration for all the modelled components is the same everywhere in the image. This is not applicable in multispectral imaging, whereas it finds useful applications in modelling chemical equilibria and reaction kinetics [ 41 ]. The intrinsic noise of the experimental technique does not allow for the implementation of unimodality constraints and the closure constraint had to be discarded because during the acquisition time, GNRs have the time to diffuse in and out from the sampled 2D section of the specimen, and a strict mass balance could not be applied.…”

Section: Resultsmentioning

confidence: 99%

An Application of Multivariate Data Analysis to Photoacoustic Imaging for the Spectral Unmixing of Gold Nanorods in Biological Tissues

et al. 2021

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Gold nanorods (GNRs) showed to be a suitable contrast agent in photoacoustics (PA), and are able to provide a tunable absorption contrast against background tissue, while a detectable PA signal can be generated from highly localized and targeted areas. A crucial issue for these imaging techniques is represented by the discrimination between exogenous and endogenous contrast and the assessment of the real PA signal magnitude. The application of image resolution/unmixing methods was implemented and optimized to recover the relative magnitude spectra and distribution maps of image constituents of the biological sample based on multivariate analysis (multivariate curve resolution—alternating least squares, MCR-ALS) in the presence of GNRs with tunable absorption properties. The proposed data analysis methodology is demonstrated on real PA images from experimental animal models and ex-vivo preparations.

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“…These theorems define when data can be safely manipulated so as not to bias the equilibrium constants while still permitting the use of a non‐negativity constrained algorithm for the absorptivity values. They leverage a version of closure that is distinct from that which is employed in soft‐modeling techiniques because it exists inherently due to the experimental design, potentially involves all concentration profiles and has weights that may not be equal to one. The secondary implication is that the precise offset of each molar absorptivity curve can be calculated from the baseline offset, the stoichiometry, and the concentrations of the stock solutions.…”

Section: Resultsmentioning

confidence: 99%

Properly handling negative values in the calculation of binding constants by physicochemical modeling of spectroscopic titration data

Kazmierczak

Griend

2019

Journal of Chemometrics

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To implement equilibrium hard‐modeling of spectroscopic titration data, the analyst must make a variety of crucial data processing choices that address negative absorbance and molar absorptivity values. The efficacy of three such methodological options is evaluated via high‐throughput Monte Carlo simulations, root‐mean‐square error surface mapping, and two mathematical theorems. Accuracy of the calculated binding constant values constitutes the key figure of merit used to compare different data analysis approaches. First, using singular value decomposition to filter the raw absorbance data prior to modeling often reduces the number of negative values involved but has little effect on the calculated binding constant despite its ability to address spectrometer noise. Second, both truncation of negative molar absorptivity values and the fast nonnegative least squares algorithms are superior to unconstrained regression because they avoid local minima; however, they introduce bias into the calculated binding constants in the presence of negative baseline offsets. Finally, we establish two theorems showing that negative values are best addressed when all the chemical solutions leading to the raw absorbance data are the result of mixing exactly two distinct stock solutions. This allows the raw absorbance data to be shifted up, eliminating negative baseline offsets, without affecting the concentration matrix, residual matrix, or calculated binding constants. Otherwise, the data cannot be safely upshifted. A comprehensive protocol for analyzing experimental absorbance datasets with is included.

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Closure constraint in multivariate curve resolution

Cited by 17 publications

References 33 publications

Application of the area correlation constraint in the MCR-ALS quantitative analysis of complex mixture samples

Application of the area correlation constraint in the MCR-ALS quantitative analysis of complex mixture samples

An Application of Multivariate Data Analysis to Photoacoustic Imaging for the Spectral Unmixing of Gold Nanorods in Biological Tissues

Properly handling negative values in the calculation of binding constants by physicochemical modeling of spectroscopic titration data

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