Principal component analysis pretreatments

As in many such problems, some form of pretreatment of the data is warranted. In all applications discussed here, the analytical data either have been untreated or have been normalized to relative concentration of each peak in the sample. Quality Assurance. Principal components analysis can be used to detect large sample differences that may be due to instrument error, noise, etc. This is illustrated by using samples 17-20 in Appendix I (Figure 6). These samples are replicate assays of a 1 1 1 1 mixture of the standard Aroclors. Fitting these data for the four samples to a 2-component model and plotting the two first principal components (Theta 1 and Theta 2 [scores] in... 

Moreda-Pineiro, A. Marcos, A. Fisher, A. Hill, S.J. Evaluation of the Effect of Data Pretreatment Procedures on Classical Pattern Recognition and Principal Components Analysis A Case Study for the Geographical Classification of Tea, J. Environ. Monit. 3(4), 352-360 (2001). 

The ultimate development in the field of sample preparation is to eliminate it completely, that is, to make a chemical measurement directly without any sample pretreatment. This has been achieved with the application of chemometric near-infrared methods to direct analysis of pharmaceutical tablets and other pharmaceutical solids (74-77). Chemometrics is the use of mathematical and statistical correlation techniques to process instrumental data. Using these techniques, relatively raw analytical data can be converted to specific quantitative information. These methods have been most often used to treat near-infrared (NIR) data, but they can be applied to any instrumental measurement. Multiple linear regression or principal-component analysis is applied to direct absorbance spectra or to the mathematical derivatives of the spectra to define a calibration curve. These methods are considered secondary methods and must be calibrated using data from a primary method such as HPLC, and the calibration material must be manufactured using an equivalent process to the subject test material. However, once the calibration is done, it does not need to be repeated before each analysis. 

Transformation of the original data to a new coordinate system is another possibility of data pretreatment. The methods are based on principal component analysis (PCA) or factor analysis (FA). The first step for these transformations is the formation of a data matrix that is derived from the original data matrix and that reflects the relationships among the data. Such derived data matrices are the variance-covariance matrix and the correlation matrix. 

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