Receptor modeling of environmental aerosol data using MLPCA-MCR-ALS

A systematic study on the effect of different error structures on pseudo‐univariate and multivariate figures of merit

“…[15][16][17][18][19][20] MLPCA-MCR-ALS is a common method in the analysis of data with a non-homoscedastic error. 21,22 Other chemometric methods for analyzing data with non-homoscedastic error-positive matrix factorization (PMF), 23 multivariate curve resolution-weighted least squares (MCR-WALS), 24 weighted Principal Component Analysis (WPCA), 25 Maximum Likelihood Principal Component Regression (MLPCR), 13 and Maximum Likelihood PARAFAC (MLPARAFAC) 26 -have been proposed that take into account the presence of this type of error structure in data. Among the mentioned methods, it has been approved that application and generalization of MLPCA-MCR-ALS are more feasible.…”

“…Multivariate curve resolution‐alternating least squares (MCR‐ALS) 12 and maximum likelihood principal component analysis–multivariate curve resolution–alternating least squares 13 (MLPCA‐MCR‐ALS) are well‐known multivariate resolution methods to overcome some chromatographic issues 5,14 (baseline/background correction, shift correction, noise reduction, and peak overlap) and to handle huge data which recorded from advanced chromatographic instruments 15–20 . MLPCA‐MCR‐ALS is a common method in the analysis of data with a non‐homoscedastic error 21,22 . Other chemometric methods for analyzing data with non‐homoscedastic error—positive matrix factorization (PMF), 23 multivariate curve resolution–weighted least squares (MCR‐WALS), 24 weighted Principal Component Analysis (WPCA), 25 Maximum Likelihood Principal Component Regression (MLPCR), 13 and Maximum Likelihood PARAFAC (MLPARAFAC) 26 —have been proposed that take into account the presence of this type of error structure in data.…”

Interval estimation in multivariate curve resolution by exploiting the principles of error propagation in linear least squares

“…Multivariate curve resolution-alternating least squares (MCR-ALS) is among the most applied bilinear decomposition algorithms usually used for the resolution of overlapping signals obtained from gas chromatography-mass spectrometry (GC-MS) [1], liquid chromatographymass spectrometry (LC-MS) [2], GC×GC-MS [3] and LC×LC-MS [4] instruments, and also by other analytical instruments [5] as well as for the mixture analysis in other fields like environmental source apportionment [6] or in hyperspectral imaging [7]. Due to its high potential for resolution of overlapping signals, MCR-ALS algorithm has found many applications in analytical and bioanalytical chemistry.…”