kernel.pls.fit {plsdof}R Documentation

Kernel Partial Least Squares fit

Description

This function computes the Kernel Partial Least Squares fit.

Usage

kernel.pls.fit(K, y, m, compute.DoF, step.size)

Arguments

K kernel matrix. This is a square matrix with dimension = number of observations. We assume that the data is centered in the feature space.
y vector of response observations.
m number of Partial Least Squares components
compute.DoF Logical variable. If compute.DoF=TRUE, the Degrees of Freedom of Partial Least Squares are computed.
step.size After how many steps should the latent components be re-orthogonalized? See below for more details.

Details

This function computed the kernel coefficients for Partial Least Squares and its Degrees of Freedom. The computation relies on a sparse matrix decomposition of the predictor variables. The sparse structure can sometimes lead to non-orthogonal latent components (due to numerical problems). To avoid this, we orthogonalize the latent components after step.size iterations.

Value

Alpha matrix of kernel coefficients. This is a matrix of size length(y) x m.
dYhat array of first derivatives of \widehat y with respect to y. The dimension of dYhat equals [m,length(y),length(y)].
Yhat matrix of fitted values. This is a matrix of size length(y) x m.
DoF vector of Degrees of Freedom.
RSS vector of residual sum of squares
sigmahat vector of estimated model error
TT matrix of latent components

Author(s)

Nicole Kraemer, Mikio L. Braun

References

Kraemer, N., Braun, M.L. (2007) "Kernelizing PLS, Degrees of Freedom, and Efficient Model Selection", Proceedings of the 24th International Conference on Machine Learning, Omni Press, 441 - 448

See Also

kernel.pls, kernel.pls.cv, kernel.pls.ic

Examples

## this is an internal function called by kernel.pls

[Package plsdof version 0.1-1 Index]