# Nolinear Transformation via B-splines

### Description

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

### Usage

1 |

### Arguments

`X` |
data matrix |

`Xtest` |
optional matrix of test data |

`deg` |
degree of the splines. Default value is 3 |

`nknot` |
vector of length |

`reduce.knots` |
Logical variable. If |

### Details

Each column of the matrix `X`

represents one variable. For
each variable, we consider the set of B-splines functions
*φ_1,...,φ_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 the transformed nonlinearly using the
B-splines function.
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 phenomenon 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` |
matrix of transformed data |

`Ztest` |
matrix of test data, if provided. Otherwise, the transformed training data is returned. |

`sizeZ` |
vector of length ncol(X). 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. Boulsteix, and G. Tutz (2008). *Penalized Partial Least Squares with Applications
to B-Spline Transformations and Functional Data*. Chemometrics and Intelligent Laboratory Systems, 94, 60 - 69. http://dx.doi.org/10.1016/j.chemolab.2008.06.009

### See Also

`ppls.splines.cv`

,`graphic.ppls.splines`

### Examples

1 2 3 |