# Eigenvector algorithm for PLS

### Description

Computes the PLS solution by eigenvector decompositions.

### Usage

1 | ```
pls_eigen(X, Y, a)
``` |

### Arguments

`X` |
X input data, centered (and scaled) |

`Y` |
Y input data, centered (and scaled) |

`a` |
number of PLS components |

### Details

The X loadings (P) and scores (T) are found by the eigendecomposition of X'YY'X. The Y loadings (Q) and scores (U) come from the eigendecomposition of Y'XX'Y. The resulting P and Q are orthogonal. The first score vectors are the same as for standard PLS, subsequent score vectors different.

### Value

`P` |
matrix with loadings for X |

`T` |
matrix with scores for X |

`Q` |
matrix with loadings for Y |

`U` |
matrix with scores for Y |

### Author(s)

Peter Filzmoser <P.Filzmoser@tuwien.ac.at>

### References

K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.

### See Also

`mvr`

### Examples

1 2 |