Factor local rank methods

Some of the local-rank analysis methods, such as evolving-factor analysis (EFA) [27-29], are more process oriented and rely on the sequential evolution of the components as a function of time or any other variable in the data set, while others, such as fixed-size moving-window-evolving-factor analysis (FSMW-EFA) [30, 31], can be applied to processes and mixtures. EFA and FSMW-EFA are the two pioneering local-rank analysis methods and can still be considered the most representative and widely used. 

Evaluating of the Distribution of Components in the Peak by Local Rank Analysis. Complementary information about the evolution of the components inside the CE peak system can be obtained from local rank analysis. In this case, instead of estimating the rank of the whole D matrix, a succession of smaller submatrices derived from D is analyzed to get the evolution of the mathematical factors throughout the system. The most widely used evolutionary methods are as follows ... 

Construction of non-random initial estimates of matrix C or S. Local rank analysis methods, such as evolving factor analysis (EFA) [1,2], or methods based on the selection of pure variables, such as simple-to-use-interactive self-modelling mixture analysis (SIMPLISMA) [18,19], can be used for this purpose. 

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. 

---