Multiset Data Analysis: Extended Multivariate Curve Resolution

Phenotypic and lipidomic characterization of primary human epidermal keratinocytes exposed to simulated solar UV radiation

“…Initialization of the MCR-ALS procedure, when applied to augmented data matrices, was performed using estimates of spectra profiles found at the purest elution times [33]. The applied constraints were non-negativity of elution and spectra profiles, and spectra normalization (equal height) [34]. Results of MCR-ALS generated a data table containing the peak areas of the elution profiles of the different resolved components in the different samples.…”

Data augmentation in food science: Synthesising spectroscopic data of vegetable oils for performance enhancement

“…To avoid confusions, this term has to be differentiated from the data matrix augmentation where other experimentally measured data matrices under different conditions are appended (row-wise, column-wise or both) to introduce a new data structure. 17 Data augmentation methods have been applied to multivariate calibration of spectroscopic data to add sample variability for a single lab validation so far. These methods were mainly based on various types of "noise" addition, otherwise referred as noise adaptation, to the original data set before calibration, 18,19 aiming to represent some of the possible variations in real spectral data.…”

Second‐order multivariate calibration with the extended bilinear model: Effect of initialization, constraints, and composition of the calibration set on the extent of rotational ambiguity

“…Multivariate curve resolution-alternating least squares (MCR-ALS) has become popular for solving the bilinear decomposition of augmented chromatographic data matrices in multicomponent analytical systems. [8][9][10][11] The decomposition is accomplished by suitable initialization and application of natural constraints during the ALS phase. The applied constraints are derived from chemical considerations, eg, nonnegativity for constituent concentrations and for spectral signals, which are known to be positive or zero but not negative, unimodality for evolving signals such as those from chromatographic or kinetic experiments, selectivity for data regions in either instrumental mode where a single constituent contributes, local rank for regions where the contributions of certain sample constituents are known to be absent, closure or mass balance for species participating in acid-base or kinetic processes, and correspondence between species and samples in multiset experiments where some constituents are known to be absent in certain samples.…”

“…The applied constraints are derived from chemical considerations, eg, nonnegativity for constituent concentrations and for spectral signals, which are known to be positive or zero but not negative, unimodality for evolving signals such as those from chromatographic or kinetic experiments, selectivity for data regions in either instrumental mode where a single constituent contributes, local rank for regions where the contributions of certain sample constituents are known to be absent, closure or mass balance for species participating in acid-base or kinetic processes, and correspondence between species and samples in multiset experiments where some constituents are known to be absent in certain samples. [8][9][10][11][12] The purpose of the constraints is to reduce or remove, if possible, any remaining ambiguity in the bilinear solutions. When this is not possible, the overall effect of the RA in second-order multivariate calibration is to introduce an additional uncertainty in the estimated analyte concentrations, beyond the one stemming from signal noise or calibration concentration uncertainties.…”