Multivariate statistics

A general comment that affects all statistical multivariate data analysis techniques, namely that each of the variables should be given equal chance to influence the outcome of the analysis. This can be achieved by scaling the variables in appropriative way. One popular method for scaling variables is autoscaling, whereby the variance of each variable is adjusted to 1. 

Fig. 17.1. Multivariate characterization with VolSurf descriptors. Molecular Interaction Fields (MIF shaded areas) are computed from the 3D-molecular structure. MIFs are transformed in a table of descriptors, and statistical multivariate analysis is performed.

Herranz, A., Serna, R, Barro, C., Martin-Alvarez, P.J., Cabezudo, M.D. (1989). Application of the statistical multivariate analysis to the differentiation of whiskies of different brands. Food... 

A different approach to mathematical analysis of the solid-state C NMR spectra of celluloses was introduced by the group at the Swedish Forest Products Laboratory (STFI). They took advantage of statistical multivariate data analysis techniques that had been adapted for use with spectroscopic methods. Principal component analyses (PCA) were used to derive a suitable set of subspectra from the CP/MAS spectra of a set of well-characterized cellulosic samples. The relative amounts of the I and I/3 forms and the crystallinity index for these well-characterized samples were defined in terms of the integrals of specific features in the spectra. These were then used to derive the subspectra of the principal components, which in turn were used as the basis for a partial least squares analysis of the experimental spectra. Once the subspectra of the principal components are validated by relating their features to the known measures of variability, they become the basis for analysis of the spectra of other cellulosic samples that were not included in the initial analysis. Here again the interested reader can refer to the original publications or the overview presented earlier. ... 

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