Kernel PLS (Dayal and MacGregor)

Fits a PLSR model with the kernel algorithm.

Usage

kernelpls.fit(X, Y, ncomp, center = TRUE, stripped = FALSE, ...)

Arguments

X

a matrix of observations. NAs and Infs are not allowed.

Y

a vector or matrix of responses. NAs and Infs are not allowed.

ncomp

the number of components to be used in the modelling.

center

logical, determines if the \(X\) and \(Y\) matrices are mean centered or not. Default is to perform mean centering.

stripped

logical. If TRUE the calculations are stripped as much as possible for speed; this is meant for use with cross-validation or simulations when only the coefficients are needed. Defaults to FALSE.

...

other arguments. Currently ignored.

Value

A list containing the following components is returned:

coefficients

an array of regression coefficients for 1, ..., ncomp components. The dimensions of coefficients are c(nvar, npred, ncomp) with nvar the number of X variables and npred the number of variables to be predicted in Y.

scores

a matrix of scores.

loadings

a matrix of loadings.

loading.weights

a matrix of loading weights.

Yscores

a matrix of Y-scores.

Yloadings

a matrix of Y-loadings.

projection

the projection matrix used to convert X to scores.

Xmeans

a vector of means of the X variables.

Ymeans

a vector of means of the Y variables.

fitted.values

an array of fitted values. The dimensions of fitted.values are c(nobj, npred, ncomp) with nobj the number samples and npred the number of Y variables.

residuals

an array of regression residuals. It has the same dimensions as fitted.values.

Xvar

a vector with the amount of X-variance explained by each component.

Xtotvar

Total variance in X.

If stripped is TRUE, only the components coefficients, Xmeans and Ymeans are returned.

Details

This function should not be called directly, but through the generic functions plsr or mvr with the argument method="kernelpls" (default). Kernel PLS is particularly efficient when the number of objects is (much) larger than the number of variables. The results are equal to the NIPALS algorithm. Several different forms of kernel PLS have been described in literature, e.g. by De Jong and Ter Braak, and two algorithms by Dayal and MacGregor. This function implements the fastest of the latter, not calculating the crossproduct matrix of X. In the Dyal & MacGregor paper, this is “algorithm 1”.

References

de Jong, S. and ter Braak, C. J. F. (1994) Comments on the PLS kernel algorithm. Journal of Chemometrics, 8, 169–174.

Dayal, B. S. and MacGregor, J. F. (1997) Improved PLS algorithms. Journal of Chemometrics, 11, 73–85.

See also

mvr plsr cppls pcr widekernelpls.fit simpls.fit oscorespls.fit

Author

Ron Wehrens and Bjørn-Helge Mevik