kcca {kernlab} | R Documentation

## Kernel Canonical Correlation Analysis

### Description

Computes the canonical correlation analysis in feature space.

### Usage

    ## S4 method for signature '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 which can be used by setting the kernel parameter to the following strings:

- `rbfdot` Radial Basis kernel function "Gaussian"

- `polydot` Polynomial kernel function

- `vanilladot` Linear kernel function

- `tanhdot` Hyperbolic tangent kernel function

- `laplacedot` Laplacian kernel function

- `besseldot` Bessel kernel function

- `anovadot` ANOVA RBF kernel function

- `splinedot` Spline kernel

The kernel parameter can also be set to a user defined function of class kernel by passing the function name as an argument.

`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 kernel function "rbfdot" and the Laplacian kernel "laplacedot".

- `degree, scale, offset` for the Polynomial kernel "polydot"

- `scale, offset` for the Hyperbolic tangent kernel function "tanhdot"

- `sigma, order, degree` for the Bessel kernel "besseldot".

- `sigma, degree` for the ANOVA kernel "anovadot".

Hyper-parameters for user defined kernels can be passed through the kpar parameter as well.

`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 space
`ycoef` | estimated coefficients for the `y` variables in the feature space

### Author(s)

Alexandros Karatzoglou
alexandros.karatzoglou@ci.tuwien.ac.at

### References

Malte Kuss, Thore Graepel
The Geometry Of Kernel Canonical Correlation Analysis
http://www.kyb.tuebingen.mpg.de/publications/pdfs/pdf2233.pdf

### See Also

`cancor`, `kpca`, `kfa`, `kha`

### Examples

    ## dummy data
    x <- matrix(rnorm(30),15)
    y <- matrix(rnorm(30),15)

    kcca(x,y,ncomps=2)

[Package kernlab version 0.9-27 Index]