Data augmentation, multivariate curve

The results presented below were obtained by multivariate curve resolution-alternating least squares (MCR-ALS). MCR-ALS was selected because of its flexibility in the application of constraints and its ability to handle either one data matrix (two-way data sets) or several data matrices together (three-way data sets). MCR-ALS has been applied to the folding process monitored using only one spectroscopic technique and to a row-wise augmented matrix, obtained by appending spectroscopic measurements from several different techniques. 

Principal component analysis (PCA) and multivariate curve resolution-alternating least squares (MCR-ALS) were applied to the augmented columnwise data matrix D1"1", as shown in Figure 11.16. In both cases, a linear mixture model was assumed to explain the observed data variance using a reduced number of contamination sources. The bilinear data matrix decomposition used in both cases can be written by Equation 11.19 ... 

Gariido, M., Lazaro, I., Larrechi, M.S., Rius F.X. (2004). Multivariate Resolution of Rank-deficient Near-infrared Sp>ectroscopy Data fron the Reaction of Curing Epwxi Resins Using the Rank Augmentation Strategy and Multivariate Curve Resolution Alternating Least Squares Approach, Analytica Chimica Acta, Vol.515. No.l, pp.65-73... 

Llamas et al. developed other spectrophotometric methods for the determination of Amaranth, Sunset Yellow, and Tartrazine in beverages [32]. The spectra of the samples (simply filtered) were recorded between 359 and 600 nm, and mixtures of pure dyes, in concentrations between 0.01 and 1.8 mg/L for Amaranth, 0.08 and 4.4 mg/L for Sunset Yellow, and 0.04 and 1.8 mg/L for Tartrazine, were disposed in a column-wise augmented data matrix. This kind of data structure, analyzed by multivariate curve resolution-alternating least squares (MCR-ALS), makes it possible to exploit the so-called second-order advantage. The MCR-ALS algorithm was applied to the experimental data under the nonnegativity and equality constraints. As a result, the concentration of each dye in the sample and their corresponding pure spectra were obtained. 

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