kernlab (version 0.9-0)

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), ...)

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
...
adittional parameters for the kpca function

Value

  • An S4 object containg the following slots:
  • kcorCorrelation coefficients in feature space
  • xcoefestimated coefficients for the x variables in the feature space
  • ycoefestimated coefficients for the y variables in the feature space
  • xvarThe canonical variates for x
  • yvarThe canonical variates for y

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