X2s {ppls}R Documentation

Nolinear transformation via B-splines

Description

This function transforms each column of a matrix using a set of B-splines functions.

Usage

X2s(X, Xtest = NULL, deg = 3, nknot = NULL,reduce.knots=FALSE)

Arguments

X A data matrix with rows corresponding to observations and columns to variables.
Xtest An optional matrix of test data with the same number of columns as X.
deg The degree of the splines. Default value is 3.
nknot A vector of length ncol(X). The jth entry determines the number of knots to be used for the jth column of X. Default value is rep(20,ncol(X)).
reduce.knots Logical variable. If TRUE, the function ensures that the transformed data does not contain any constant column. See below for more details. Default value is FALSE.

Details

Each column of the matrix X represents one variable. For each variable, we consider the set of B-splines functions phi_1,...,phi_K that are determined by the degree deg of the splines and the number nknot of knots. The knots are equidistantly based on the range of the variable. The data and – if available – the test data is transformed nonlinearly using the B-splines functions. For a large amount of knots, it is possible that some columns of the transformed matrix Z only contain zeroes. If this is the case for one variable and if reduce.knots=TRUE, the amount of knots is reduced until this does not occur anymore. Note that the penalized PLS algorithm runs correctly for constant columns in Z, unless you scale the columns of the data.

Value

Z The matrix of transformed data with ncol(X) x (nknot-deg-1) columns.
Ztest The matrix of test data, if provided. Otherwise, the transformed training data is returned.
sizeZ A vector of length ncol(X), where each component contains the number of basis functions for each column of X.

Note

Depending on the degrees of the splines - there must be minimum number of knots. If nknot contains too few knots, the function automatically increases the number.

Author(s)

Nicole Kraemer

References

C. de Boor (1978) "A practical guide to splines", Springer.

N. Kraemer, A.-L. Boulesteix, G. Tutz (2007) "Penalized Partial Least Squares with Applications to B-Splines Transformations and Functional Data", preprint

available at http://ml.cs.tu-berlin.de/~nkraemer/publications.html

See Also

ppls.splines.cv

Examples

X<-matrix(rnorm(100),ncol=5)
Xtest<-matrix(rnorm(300),ncol=5)
dummy<-X2s(X,Xtest)

[Package ppls version 1.0 Index]