Advantages of soft versus hard constraints in self-modeling curve resolution problems. Penalty alternating least squares (P-ALS) extension to multi-way problems.
An extension to the penalty alternating least squares (P-ALS) method, called multi-way penalty alternating least squares (NWAY P-ALS), is presented. Optionally, hard constraints (no deviation from predefined constraints) or soft constraints (small deviations from predefined constraints) were applied through the application of a row-wise penalty least squares function. NWAY P-ALS was applied to the multi-batch near-infrared (NIR) data acquired from the base catalyzed esterification reaction of acetic anhydride in order to resolve the concentration and spectral profiles of l-butanol with the reaction constituents. Application of the NWAY P-ALS approach resulted in the reduction of the number of active constraints at the solution point, while the batch column-wise augmentation allowed hard constraints in the spectral profiles and resolved rank deficiency problems of the measurement matrix. The results were compared with the multi-way multivariate curve resolution (MCR)-ALS results using hard and soft constraints to determine whether any advantages had been gained through using the weighted least squares function of NWAY P-ALS over the MCR-ALS resolution.
Richards
Selena
S
Department of Biomolecular Medicine, Division of Surgery, Oncology, Reproductive Biology, and Anaesthetics, Faculty of Medicine, Imperial College London, Sir Alexander Fleming Building, South Kensington, London SW 7 2AZ, United Kingdom.
Miller
Robert
R
Gemperline
Paul
P
D020001:1-Butanol / Q000737:chemistry; D000089:Acetic Anhydrides / Q000737:chemistry; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D008956:Models, Chemical; D015233:Models, Statistical; D011725:Pyridines / Q000737:chemistry; D019265:Spectroscopy, Near-Infrared / Q000379:methods*
D000089:Acetic Anhydrides; D011725:Pyridines; C031800:acetic anhydride; D020001:1-Butanol; C023666:pyridine