Self modeling

A method of resolution that makes a very few a priori assumptions is based on principal components analysis. The various forms of this approach are based on the self-modeling curve resolution developed in 1971 (55). The method requites a data matrix comprised of spectroscopic scans obtained from a two-component system in which the concentrations of the components are varying over the sample set. Such a data matrix could be obtained, for example, from a chromatographic analysis where spectroscopic scans are obtained at several points in time as an overlapped peak elutes from the column. 

W.H. Lawton and E A. Sylvestre, Self modeling curve resolution. Technometrics, 13 (1971) 617-633. 

B.G.M. Vandeginste, W.Derks andG. Kateman, Multicomponent self modelling curve resolution in high performance liquid chromatography by iterative target transformation analysis. Anal. Chim. Acta, 173 (1985) 253-264. 

W. Windig and J. Guilement, Interactive self-modeling mixture analysis. Anal. Chem., 63... 

W. Windig, C.E. Heckler, FA. Agblevor and R.J. Evans, Self-modeling mixture analysis of categorized pyrolysis mass-spectral data with the Simplisma approach. Chemom. Intell. Lab. Syst., 14(1992) 195-207. 

W. Windig and D.A. Stephenson, Self-modeling mixture analysis of second-derivative near-infrared spectral data using the Simplisma approach. Anal. Chem., 64 (1992) 2735-2742. 

More commonly, we are faced with the need for mathematical resolution of components, using their different patterns (or spectra) in the various dimensions. That is, literally, mathematical analysis must supplement the chemical or physical analysis. In this case, we very often initially lack sufficient model information for a rigorous analysis, and a number of methods have evolved to "explore the data", such as principal components and "self-modeling analysis (21), cross correlation (22). Fourier and discrete (Hadamard,. . . ) transforms (23) digital filtering (24), rank annihilation (25), factor analysis (26), and data matrix ratioing (27). 

P.J. Gemperline and E. Cash, Advantages of soft versus hard constraints in self-modeling curve resolution problems. Alternating Least squares with penalty functions. Anal. Chem., 75, 4236 (2003). 

SMCR self-modeling curve resolution UV-vis ultraviolet-visible... 

SIMPLISMA simple-to-nse interactive self-modeling analysis... 

R Tauler, S Lacorte, D Barcelo. Application of multivariate self-modeling curve resolution to the quatitation of trace levels of organophosphorus pesticides in natural waters from interlaboratory studies. J Chromatogr A 730 177-183, 1996. 

DeBraekeleer, K. Cuesta Sanchez, F. Hailey, P.A. etal., Influence and correction of temperature perturbations on NIR spectra during the monitoring of a polymorph conversion process prior to self-modelling mixture analysis /. Pharm. Biomed. Anal. 1997, 17, 141-152. 

Figure 4.25 Infrared images and self-modeling spectra of components of butter-bacteria before (on the left) and after (on the right) FT filtering.

The relative absorbance values obtained by these self-modeling procedures are proportional to concentrations of the components in the mixtures and are used as the first estimates for concentrations. The method of alternating least squares14 is then applied to the data. In this method, the mixture spectra in the absorbance matrix, A, are written in terms of Beer s law as... 

The problem of baseline interferences in self-modeling mixture analysis has been addressed recently by using a combination of conventional and second-derivative data in the SIMPLISMA method.13 In that approach, purity peaks could be obtained from either conventional or second-derivative spectra depending upon the spectral bandwidths, and the baselines were extracted as a separate component from the SIMPLISMA analysis. As mentioned earlier in the present report, the pixel-to-pixel variations produce many different shaped baselines, which cannot be accounted for by a single extracted baseline. It seems reasonable that second-derivative spectra could be used effectively to characterize the distribution of chemical components,... 

Extension of Self-Modeling Curve Resolution to Multiway Data MCR-ALS Simultaneous Analysis of Multiple... 

There are many chemometric methods to build initial estimates some are particularly suitable when the data consists of the evolutionary profiles of a process, such as evolving factor analysis (see Figure 11.4b in Section 11.3) [27, 28, 51], whereas some others mathematically select the purest rows or the purest columns of the data matrix as initial profiles. Of the latter approach, key-set factor analysis (KSFA) [52] works in the FA abstract domain, and other procedures, such as the simple-to-use interactive self-modeling analysis (SIMPLISMA) [53] and the orthogonal projection approach (OPA) [54], work with the real variables in the data set to select rows of purest variables or columns of purest spectra, that are most dissimilar to each other. In these latter two methods, the profiles are selected sequentially so that any new profile included in the estimate is the most uncorrelated to all of the previously selected ones. 

Jiang, J.H. and Ozaki, Y., Self-modeling curve resolution (SMCR) principles, techniques, and applications, Appl. Spectr. Rev., 37, 321-345, 2002. 

Tauler, R., Izquierdo-Ridorsa, A., and Casassas, E., Simultaneous analysis of several spectroscopic titrations with self-modeling curve resolution, Chemom. Intell. Lab. Sys., 18, 293-300, 1993. 

Wentzell, P.D., Wang, J., Loucks, L.F., and Miller, K.M., Direct optimization of self modeling curve resolution application to the kinetics of the permanganate-oxalic acid reaction, Can. J. Chem., 76, 1144-1155, 1998. 

Gemperline, P.J., Computation of the range of feasible solutions in self-modeling curve resolution algorithms, Anal. Chem., 71, 5398-5404, 1999. 

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