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)
... adittional 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 containg 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 0.9-8 Index]