Wide Kernel PLS (Rännar et al.)

Fits a PLSR model with the wide kernel algorithm.

Usage

widekernelpls.fit(
  X,
  Y,
  ncomp,
  center = TRUE,
  stripped = FALSE,
  tol = .Machine$double.eps^0.5,
  maxit = 100,
  ...
)

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.
tol: numeric. The tolerance used for determining convergence in the algorithm.
maxit: positive integer. The maximal number of iterations used in the internal Eigenvector calculation.
...: 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="widekernelpls". The wide kernel PLS algorithm is efficient when the number of variables is (much) larger than the number of observations. For very wide X, for instance 12x18000, it can be twice as fast as kernelpls.fit and simpls.fit. For other matrices, however, it can be much slower. The results are equal to the results of the NIPALS algorithm.

Note

The current implementation has not undergone extensive testing yet, and should perhaps be regarded as experimental. Specifically, the internal Eigenvector calculation does not always converge in extreme cases where the Eigenvalue is close to zero. However, when it does converge, it always converges to the same results as kernelpls.fit, up to numerical inacurracies.

The algorithm also has a bit of overhead, so when the number of observations is moderately high, kernelpls.fit can be faster even if the number of predictors is much higher. The relative speed of the algorithms can also depend greatly on which BLAS and/or LAPACK library is linked against.

References

Rännar, S., Lindgren, F., Geladi, P. and Wold, S. (1994) A PLS Kernel Algorithm for Data Sets with Many Variables and Fewer Objects. Part 1: Theory and Algorithm. Journal of Chemometrics, 8, 111–125.

Author

Bjørn-Helge Mevik