Performance and validation of MCR-ALS with quadrilinear constraint in the analysis of noisy datasets

This study explores the effect of noise propagation on the resolution capability of multivariate curve resolution-alternating least squares with a recently developed quadrilinearity constraint (MCR-ALSQ). To investigate the effect of application of the quadrilinearity constraint, four environmental profiles were simulated and three types of noise viz. homoscedastic, heteroscedastic, and constant-proportional noise at three different levels were added to the simulated dataset. The profiles recovered with MCR-ALSQ were compared with the ones recovered by bilinear MCR-ALS (MCR-ALSB). The effect of maximum likelihood principal component analysis (MLPCA) as a pre-processing step in MCR-ALSQ (MLPCA–MCR-ALSQ), and MCR-ALSB (MLPCA–MCR-ALSB) analysis was also studied and results were compared with ones obtained with MCR-ALSQ and MCR-ALSB models. The recovery and similarity of the resolved profiles with theoretical ones were assessed in terms of similarity coefficient (r2) and similarity angle (θ). The results of this study conclude that MCR-ALSQ is appropriate to analyze four-way quadrilinear datasets, and that the use of MLPCA as a pre-processing step before MCR-ALSQ improves the resolution profiles to a great extent even in the presence of high levels of noise (heteroscedastic, and constant-proportional).