Orthogonal projection approach

F.C. Sanchez, J. Toft, B. van den Bogaert and D.L. Massart, Orthogonal projection approach applied to peak purity assessment. Anal. Chem., 68 (1996) 79-85. 

By applying the orthogonal projection approach, the following Qui, QU2, Rui and Ru2 matrices are obtained ... 

Matrix D is calculated and the application of the orthogonal projection approach leads to QD, QD2, RDi, RD2, Ilfu matrices. 

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

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). 

F.C. Sanchez, S.C. Rutan, M.D. Gil Garcia and D.L. Massart, Resolution of Multicomponent Overlapped Peaks by the Orthogonal Projection Approach, Evolving Factor Analysis and Window Factor Analysis, Chemom. Intell. Labs. Syst. 36 (1997), 153-164. 

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