# kcca

##### Kernel Canonical Correlation Analysis

Computes the canonical correlation analysis in feature space.

- Keywords
- multivariate

##### Usage

```
## S3 method for class 'matrix':
kcca(x, y, kernel="rbfdot", kpar=list(sigma=0.1),
gamma = 0.1, ncomps = 10, ...)
```

##### Arguments

- x
- a matrix containing data index by row
- y
- a matrix containing data index by row
- kernel
- the kernel function used in training and predicting. This parameter can be set to any function, of class kernel, which computes a inner product in feature space between two vector arguments. kernlab provides the most popular kernel functions
- kpar
- the list of hyper-parameters (kernel parameters).
This is a list which contains the parameters to be used with the
kernel function. Valid parameters for existing kernels are :
`sigma`

inverse kernel width for the Radial Basis

- gamma
- regularization parameter (default : 0.1)
- ncomps
- number of canonical components (default : 10)
- ...
- additional parameters for the
`kpca`

function

##### Details

The kernel version of canonical correlation analysis. Kernel Canonical Correlation Analysis (KCCA) is a non-linear extension of CCA. Given two random variables, KCCA aims at extracting the information which is shared by the two random variables. More precisely given $x$ and $y$ the purpose of KCCA is to provide nonlinear mappings $f(x)$ and $g(y)$ such that their correlation is maximized.

##### Value

- An S4 object containing the following slots:
kcor Correlation coefficients in feature space xcoef estimated coefficients for the `x`

variables in the feature spaceycoef estimated coefficients for the `y`

variables in the feature space

##### References

Malte Kuss, Thore Graepel
*The Geometry Of Kernel Canonical Correlation Analysis*

##### See Also

##### Examples

```
## dummy data
x <- matrix(rnorm(30),15)
y <- matrix(rnorm(30),15)
kcca(x,y,ncomps=2)
```

*Documentation reproduced from package kernlab, version 0.9-13, License: GPL-2*

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