kcca function

Kernel Canonical Correlation Analysis

Computes the canonical correlation analysis in feature space.

## 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.

Returns

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

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/

Author(s)

Alexandros Karatzoglou

alexandros.karatzoglou@ci.tuwien.ac.at

See Also

cancor, kpca, kfa, kha

Examples

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

kcca(x,y,ncomps=2)