Detrended principal components

There have been attempts to deal with the issue of nonlinearity in data sets. Detrended principal components (DPC) use a polynomial expression to remove the nonlinear relationships from the PCA axes. DPC are useful for data sets of moderate nonlinearity. Detrended correspondence analysis uses a more complex algorithm to eliminate the nonlinearity but requires a more complex computation. Nonmetric multidimensional scaling (NMDS) is a robust method that deals with nonlinearities by using ranks. 

A variety of multivariate techniques (Q-mode and R-mode cluster analysis. Principal component analysis (PCA) and Detrended Correspondence Analysis (DCA)) were... 

More complex means of attacking the particle size question have also been attempted. These include experiments using mathematical modeling for simultaneous removal of particle size and water [29], the use of Fourier deconvolution [30], multiplicative scatter corrections [31 ], and principal components elimination [32]. Barnes et al. [33] introduced a procedure termed detrending that uses standard normal variate (SNV) with polynomial baseline correction [34]. These corrections for particle size may not always improve accuracy of NIRS analysis for two reasons. First, none of these procedures does a perfect job of removing particle size effects independent of absorption information. Second, particle size may be useful information in the calibration even though linear mathematics is used to derive the analytical equation. 

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