kernlab (version 0.9-33)

kcca: Kernel Canonical Correlation Analysis

Description

Computes the canonical correlation analysis in feature space.

Usage

# S4 method for matrix
kcca(x, y, kernel="rbfdot", kpar=list(sigma=0.1),
gamma = 0.1, ncomps = 10, ...)

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

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

Author

Alexandros Karatzoglou

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

See Also

cancor, kpca, kfa, kha

Examples

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

kcca(x,y,ncomps=2)