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kcca

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)

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/

See Also

Examples

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

kcca(x,y,ncomps=2)
kernlab

Kernel-Based Machine Learning Lab

v0.9-29
GPL-2
Authors
Alexandros Karatzoglou [aut, cre], Alex Smola [aut], Kurt Hornik [aut], National ICT Australia (NICTA) [cph], Michael A. Maniscalco [ctb, cph], Choon Hui Teo [ctb]
Initial release

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