Singular value decomposition component estimation

TLD uses multiple standards instead of one as in RAFA. The algorithm is similar to RAFA in that an eigenvalue problem is determined and solved through the use of singular-value decomposition. One important result of using second-order approaches such as RAFA and TLD is that the results of singular-value decomposition give estimates of the pure component response patterns which can be compared to the true response patterns. This ability allows users to check the performance of the procedure and identify components in the sample. 

In principle both the classical and the inverse approach use a multivariate data set. But in the classical approach the variance is minimised, whereas in the inverse approach one tries to find an equilibrium between bias and variance. Therefore the bias is reduced and by the procedure of predictive receivable error sum of squares either via a singular value decomposition or the bidiagonalisation method estimated values, either according to principle component regression or partial least squares, are found. The multilinear regression on the other hand will find the best linear unbiased estimation as an approach to a true concentration. Besides applications in absorption spectroscopy, fluorescence spectra can also be evaluated [74]. 

To estimate the number of components, singular value decomposition (SVD) was applied to the IR data X measured during the PVA degradation process. Using singular values from 1 to 3, 96.7 % of aU variance was captured extending the range to 1 allowed the capture of 98.4 % of the variance (Fig. 9). 

Determination of the number of components in the data set. Can be known beforehand or estimated by other methods, such as singular value decomposition (SVD) [17]. 

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