# kcca: Kernel Canonical Correlation Analysis In kernlab: Kernel-Based Machine Learning Lab

 kcca 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
https://www.microsoft.com/en-us/research/publication/the-geometry-of-kernel-canonical-correlation-analysis/

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

### Examples

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

kcca(x,y,ncomps=2)

```

kernlab documentation built on Feb. 16, 2023, 10:13 p.m.