Advantages of Soft versus Hard Constraints in Self-Modeling Curve Resolution Problems. Penalty Alternating Least Squares (P-ALS) Extension to Multi-way Problems

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Abstract:

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.

Keywords: ALS; ALTERNATING LEAST SQUARES; ESTERIFICATION REACTIONS; MCR; MULTIVARIATE CURVE RESOLUTION; SELF-MODELING CURVE RESOLUTION; SMCR; SOFT CONSTRAINTS

Document Type: Research Article

DOI: http://dx.doi.org/10.1366/000370208783575645

Affiliations: 1: 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 2: Department of Chemistry, East Carolina University, Greenville, North Carolina 27858

Publication date: February 1, 2008

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