Orthogonal projection approach OPA

A basic assumption of OPA is that the purest spectra are mutually more dissimilar than the corresponding mixture spectra. Therefore, OPA uses a dissimilarity criterion to find the number of components and the corresponding purest spectra. Spectra are sequentially selected, taking into account their dissimilarity. The dissimilarity of spectrum i is defined as the determinant of a dispersion matrix Y,. In general, matrices Y, consist of one or more reference spectra, and the spectrum measured at the /th elution time. 

A dissimilarity plot is then obtained by plotting the dissimilarity values, dj, as a function of the retention time i. Initially, each p 2 matrix Y, consists of two columns the reference spectrum, which is the mean (average) spectram (normalised to unit length) of matrix X, and the spectrum at the /th retention time. The spectrum with the highest dissimilarity value is the least correlated with the mean spectrum, and it is the first spectrum selected, x, . Then, the mean spectrum is replaced by x, as reference in matrices Y, (Y, = [x j x,]), and a second dissimilarity plot is obtained by applying eq. (34.14). The spectrum most dissimilar with x, is selected (x 2) and added to matrix Y,-. Therefore, for the determination of the third dissimilarity plot Y, contains three columns [x, x 2 /] wo reference spectra and the spectmm at the /th retention time. 

In summary, the selection procedure consists of three steps (1) compare each spectrum in X with all spectra already selected by applying eq. (34.14). Initially, when no spectrum has been selected, the spectra are compared with the average spectrum of matrix X (2) plot of the dissimilarity values as a function of the retention time (dissimilarity plot) and (3) select the spectrum with the highest dissimilarity value by including it as a reference in matrix Y,-. The selection of the spectra is finished when the dissimilarity plot shows a random pattern. It is considered that there are as many compounds as there are spectra. Once the purest spectra are available, the data matrix X can be resolved into its spectra and elution profiles by Alternating Regression explained in Section 34.3.1. 

By way of illustration, let us consider the separation of 0.2% prednisone in etrocortysone eluting with a chromatographic resolution equal to 0.8 [30] (Fig. 34.40). The dissimilarity of each spectrum with respect to the mean spectrum is plotted in Fig. 34.41a. Two clearly differentiated peaks with maxima around times 46 and 63 indicate the presence of at least two compounds. In this case, the 

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De Braekeleer, K., and Massart, D. L. (1997), Evaluation of the orthogonal projection approach (OPA) and the SIMPLISMA approach on the Windig standard spectral data sets, Chemomet. Intell. Lab. Syst., 39,127-141. 

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. 

MEKC-DAD data (54). Studies from Kaniansky and coworkers have focused on using factor analysis, including ITTFA, WFA, and orthogonal projection approach (OPA), for the feasible identification of orotic acid at low concentration level in urine matrices (55, 56). The mathematical resolution of anionic surfactants that cannot be separated electrophoretically has been accomplished by OPA-ALS (57). 

OPA orthogonal projection approach Q number of increments per sample... 

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