dots.rd

这是核学习的一个基础软件包

\name{dots}
\alias{dots}
\alias{rbfdot}
\alias{polydot}
\alias{tanhdot}
\alias{vanilladot}
\alias{kpar}
\alias{show,kernel-method}
\title{Kernel Functions}
\description{
  The kernel generating functions provided in kernlab. \cr
  The Gaussian kernel \eqn{k(x,x') = \exp(-\sigma \|x - x'\|^2)} \cr
  the Polynomial kernel \eqn{k(x,x') = (scale <x, x'> + offset)^degree}.\cr
  the Linear kernel \eqn{k(x,x') = <x, x'>}\cr
  and the  Hyperbolic tangent kernel \eqn{k(x, x') = \tanh(scale <x, x'> + offset)}
}
\usage{
rbfdot(sigma = 1)

polydot(degree = 1, scale = 1, offset = 1)

tanhdot(scale = 1, offset = 1)

vanilladot()
}

\arguments{
  \item{sigma}{The inverse kernel width used by the Gaussian kernel}
  \item{degree}{The degree of the polynomial kernel. This has to be an integer.}
  \item{scale}{The scaling parameter is a convenient way of normalizing
    patterns without the need to modify the data itself}
  \item{offset}{The offset used in a polynomial or hyperbolic tangent kernel}
}
\details{
  The kernel generating function are used to initialize a kernel
  function
  which calculates the dot (inner) product between two feature vectors in a
  Hilbert Space. These functions can be based as a \code{kernel} argument on almost all
  functions in kernlab (eg. \code{ksvm}, \code{kpca}  etc).
  Although using one of the above mentioned existing kernel functions as a
  \code{kernel} argument in various functions in kernlab has the
  advantage that use of optimize kernel utilities methods are used
  any other function implementing a dot product of class kernel can also be used as a kernel
  argument. This allows the user to use test an develop special kernels
  for a given data set and algorithm.
  }
\value{
 Return an S4 object of class \code{kernel} which extents the
 \code{function} class. The resulting function implements the given
 kernel calculating the inner (dot) product between two vectors.
 \item{kpar}{a list containing the kernel parameters (hyperparameters)
   used.}
 the kernel parameters can be accessed by the \code{kpar} function.
 }

\author{Alexandros Karatzoglou\cr
  \email{[e-mail]}}

\note{If the offset in the Polynomial kernel is set to $0$, we obtain homogeneous polynomial
  kernels, for positive values, we have inhomogeneous
  kernels. Note that for negative values the kernel does not satisfy Mercer's
  condition and thus the optimizers may fail. \cr

  In the Hyperbolic tangent kernel if the offset is negative the likelihood of obtaining a kernel
  matrix that is not positive definite is much higher (since then even some
  diagonal elements may be negative), hence if this kernel has to be used, the
  offset should always be positive. Note, however, that this is no guarantee
  that the kernel will be positive.
}




\seealso{ \code{\link{kernelMatrix} }, \code{\link{kernelMult}}, \code{\link{kernelPol}}}
\examples{
rbfkernel <- rbfdot(sigma = 0.1)
rbfkernel

kpar(rbfkernel)

## create two vectors
x <- rnorm(10)
y <- rnorm(10)

## calculate dot product
rbfkernel(x,y)

}
\keyword{symbolmath}