# rcc: Regularized Canonical Correlation Analysis In CCA: Canonical Correlation Analysis

## Description

The function performs the Regularized extension of the Canonical Correlation Analysis to seek correlations between two data matrices when the number of columns (variables) exceeds the number of rows (observations)

## Usage

 `1` ```rcc(X, Y, lambda1, lambda2) ```

## Arguments

 `X` numeric matrix (n * p), containing the X coordinates. `Y` numeric matrix (n * q), containing the Y coordinates. `lambda1` Regularization parameter for X `lambda2` Regularization parameter for Y

## Details

When the number of columns is greater than the number of rows, the matrice X'X (and/or Y'Y) may be ill-conditioned. The regularization allows the inversion by adding a term on the diagonal.

## Value

A list containing the following components:

 `corr` canonical correlations `names` a list containing the names to be used for individuals and variables for graphical outputs `xcoef` estimated coefficients for the 'X' variables as returned by `cancor()` `ycoef` estimated coefficients for the 'Y' variables as returned by `cancor()` `scores` a list returned by the internal function comput() containing individuals and variables coordinates on the canonical variates basis.

## Author(s)

Sébastien Déjean, Ignacio González

## References

Leurgans, Moyeed and Silverman, (1993). Canonical correlation analysis when the data are curves. J. Roy. Statist. Soc. Ser. B. 55, 725-740.

Vinod (1976). Canonical ridge and econometrics of joint production. J. Econometr. 6, 129-137.

## See Also

`cc`, `estim.regul`, `plt.cc`

## Examples

 ```1 2 3 4 5``` ```data(nutrimouse) X=as.matrix(nutrimouse\$gene) Y=as.matrix(nutrimouse\$lipid) res.cc=rcc(X,Y,0.1,0.2) plt.cc(res.cc) ```

### Example output ```Loading required package: fda
Loading required package: splines
Loading required package: Matrix

Attaching package: 'fda'

The following object is masked from 'package:graphics':

matplot

Loading required package: fields
Loading required package: spam
Loading required package: dotCall64
Loading required package: grid
Spam version 2.2-0 (2018-06-19) is loaded.
Type 'help( Spam)' or 'demo( spam)' for a short introduction
and overview of this package.
Help for individual functions is also obtained by adding the
suffix '.spam' to the function name, e.g. 'help( chol.spam)'.

Attaching package: 'spam'

The following object is masked from 'package:Matrix':

det

The following objects are masked from 'package:base':

backsolve, forwardsolve

Loading required package: maps
See www.image.ucar.edu/~nychka/Fields for
a vignette and other supplements.
```

CCA documentation built on March 1, 2021, 9:06 a.m.