Eigenvector quantitation methods

Many of these methods use PCA as a spectral data compression technique. As discussed in Chapter 4, PCA produces a reduced representation of the training set spectra based on the variations between the samples (refer to Chapter 4, Eigenvector Quantitation Methods section). Remember that PCA decomposes a set of spectra into their most common variations (factors) and produces a small set of well-defined numbers (scores) for each sample that represent the amount of each variation present in the spectrum. Similar to using the scores for creating a quantitative calibration equation, they can also be used for discrimination because they provide an accurate description of the entire set of training spectra. However, many of the methods listed previously utilize only the first few significant factors for discrimination. In many cases, only the first two factors are used. Thus,... 

Duckworth [131] and others [132] have reviewed quantitative spectroscopic analysis, including evaluations of classical quantitation methods (LSR, CLS, ILS) and eigenvector quantitation methods (PCR, PLS, factor analysis). Another useful review dealing with chemometrics (to spectra) is ref. [137]. 

The use of mathematical and statistical modeling methods to relate chemical data sets to the state of the chemical system is referred to as chemometrics. A key figure in the development of chemometrics and its application to industrial problems has been B.R. Kowalski [18, 147, 319] who led the Center for Process Analytical Chemistry (CPAC) that was established in 1984. To aid qualitative and quantitative analysis of chemical data, Eigenvector Technologies Inc., a developer of independent commercial software, has provided a number of software solutions, primarily as a Matlab Toolbox [328]. 

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