kernlab (version 0.9-24)

kcca: Kernel Canonical Correlation Analysis

Description

Computes the canonical correlation analysis in feature space.

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 :

• sigmainverse 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

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

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.

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)