Factor full-rank method

Basically, we make a distinction between methods which are carried out in the space defined by the original variables (Section 34.4) or in the space defined by the principal components. A second distinction we can make is between full-rank methods (Section 34.2), which consider the whole matrix X, and evolutionary methods (Section 34.3) which analyse successive sub-matrices of X, taking into account the fact that the rows of X follow a certain order. A third distinction we make is between general methods of factor analysis which are applicable to any data matrix X, and specific methods which make use of specific properties of the pure factors. 

Either PLS or PCR can be used to compute b, at less than full rank by discarding factors associated with noise. Because of the banded diagonal structure of the transformation matrix used by PDS, localized multivariate differences in spectral response between the primary and secondary instrument can be accommodated, including intensity differences, wavelength shifts, and changes in spectral bandwidth. The flexibility and power of the PDS method has made it one of the most popular instrument standardization methods. 

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