Alternating least squares MCR-ALS

The next subsection deals first with aspects common to all resolution methods. These include (1) issues related to the initial estimates, i.e., how to obtain the profiles used as the starting point in the iterative optimization, and (2) issues related to the use of mathematical and chemical information available about the data set in the form of so-called constraints. The last part of this section describes two of the most widely used iterative methods iterative target transformation factor analysis (ITTFA) and multivariate curve resolution-alternating least squares (MCR-ALS). 

Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS)... 

Multivariate curve resolution-alternating least squares (MCR-ALS) uses an alternative approach to iteratively find the matrices of concentration profiles and instrumental responses. In this method, neither the C nor the ST matrix have priority over each other, and both are optimized at each iterative cycle [7, 21, 42], The general operating procedure of MCR-ALS includes the following steps ... 

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 ... 

Multivariate curve resolution-alternating least squares (MCR-ALS) is an algorithm that fits the requirements for image resolution [71, 73-75]. MCR-ALS is an iterative method that performs the decomposition into the bilinear model D = CS by means of an alternating least squares optimization of the matrices C and according to the following steps ... 

FIGURE 9.6. Scheme of steps of multivariate curve resolution based on alternating least squares (MCR-ALS procedure). 

An implementation of Multivariate Curve Resolution Alternating Least Squares (MCR-ALS) can be downloaded from http //www.ub.es/gesq/mcr/ mcr.htm.7 MCR is also available in The Unscrambler (Camo Inc., Wood-bridge, New Jersey, USA). 

Garrido, M., Rius, F.X., Larrechi, M.S. (2008). Multivariate Curve Resolution-alternating Least Squares (MCR-ALS) Applied to Spectroscopic Data from Monitoring Chemical Reaction Processes, Anal. Bioanal. Chem., Vol.390, No.8,... 

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. 

MCR-ALS Multivariate curve resolution alternating least squares... 

---