R: Kernel Matrix functions

kernelMatrix {kernlab}

R Documentation

Kernel Matrix functions

Description

kernelMatrix calculates the kernel matrix K_{ij} = k(x_i,x_j) or K_{ij} = k(x_i,y_j).
kernelPol computes the quadratic kernel expression H = z_i z_j k(x_i,x_j), H = z_i k_j k(x_i,y_j).
kernelMult calculates the kernel expansion f(x_i) = sum_{i=1}^m z k(x_i,x_j)

Usage

## S4 method for signature 'kernel':
kernelMatrix(kernel, x, y = NULL)

## S4 method for signature 'kernel':
kernelPol(kernel, x, y = NULL, z, k = NULL)

## S4 method for signature 'kernel':
kernelMult(kernel, x, y = NULL, z, blocksize = 256)

Arguments

`kernel`	the kernel function to be used to calculate the kernel matrix. This has to be a function of class `kernel`
`x`	a data matrix to be used to calculate the kernel matrix
`y`	second data matrix to calculate the kernel matrix
`z`	a suitable vector or matrix
`k`	a suitable vector or matrix
`blocksize`	the kernel expansion computations are done block wise to avoid storing the kernel matrix into memory. `blocksize` defines the size of the computational blocks.

Details

Common functions used during kernel based computations.
This kernel parameter can be set to any function, of class kernel, which computes a dot product between two vector arguments. kernlab provides the most popular kernel functions which can be initialized by using the following functions:

rbfdot Radial Basis kernel function
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

(see example.)

Value

kernelMatrix returns a symmetric diagonal semi-definite matrix. kernelPol returns a matrix. kernelMult{usually returns a one-column matrix}

Author(s)

Alexandros Karatzoglou
alexandros.karatzoglou@ci.tuwien.ac.at

Examples

## use the spam data
data(spam)
dt <- as.matrix(spam[c(10:20,3000:3010),-58])

## initialize kernel function 
rbf <- rbfdot(sigma = 0.05)
rbf

## calculate kernel matrix
kernelMatrix(rbf, dt)

yt <- as.matrix(as.integer(spam[c(10:20,3000:3010),58]))
yt[yt==2] <- -1

## calculate the quadratic kernel expression
kernelPol(rbf, dt, ,yt)

## calculate the kernel expansion
kernelMult(rbf, dt, ,yt)

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