kernlab (version 0.9-27)

# dots: Kernel Functions

## Description

The kernel generating functions provided in kernlab. The Gaussian RBF kernel $$k(x,x') = \exp(-\sigma \|x - x'\|^2)$$ The Polynomial kernel $$k(x,x') = (scale <x, x'> + offset)^{degree}$$ The Linear kernel $$k(x,x') = <x, x'>$$ The Hyperbolic tangent kernel $$k(x, x') = \tanh(scale <x, x'> + offset)$$ The Laplacian kernel $$k(x,x') = \exp(-\sigma \|x - x'\|)$$ The Bessel kernel $$k(x,x') = (- Bessel_{(\nu+1)}^n \sigma \|x - x'\|^2)$$ The ANOVA RBF kernel $$k(x,x') = \sum_{1\leq i_1 \ldots < i_D \leq N} \prod_{d=1}^D k(x_{id}, {x'}_{id})$$ where k(x,x) is a Gaussian RBF kernel. The Spline kernel $$\prod_{d=1}^D 1 + x_i x_j + x_i x_j min(x_i, x_j) - \frac{x_i + x_j}{2} min(x_i,x_j)^2 + \frac{min(x_i,x_j)^3}{3}$$ \ The String kernels (see stringdot.

## Usage

rbfdot(sigma = 1)polydot(degree = 1, scale = 1, offset = 1)tanhdot(scale = 1, offset = 1)vanilladot()laplacedot(sigma = 1)besseldot(sigma = 1, order = 1, degree = 1)anovadot(sigma = 1, degree = 1)splinedot()

## Arguments

sigma

The inverse kernel width used by the Gaussian the Laplacian, the Bessel and the ANOVA kernel

degree

The degree of the polynomial, bessel or ANOVA kernel function. This has to be an positive integer.

scale

The scaling parameter of the polynomial and tangent kernel is a convenient way of normalizing patterns without the need to modify the data itself

offset

The offset used in a polynomial or hyperbolic tangent kernel

order

The order of the Bessel function to be used as a kernel

## Value

Return an S4 object of class kernel which extents the function class. The resulting function implements the given kernel calculating the inner (dot) product between two vectors.

kpar

a list containing the kernel parameters (hyperparameters) used.

The kernel parameters can be accessed by the kpar function.

## Details

The kernel generating functions 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 passed as a kernel argument on almost all functions in kernlab(e.g., ksvm, kpca etc).

Although using one of the existing kernel functions as a kernel argument in various functions in kernlab has the advantage that optimized code is used to calculate various kernel expressions, 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 and develop special kernels for a given data set or algorithm. For details on the string kernels see stringdot.

stringdot, kernelMatrix , kernelMult, kernelPol

## Examples

Run this code
# NOT RUN {
rbfkernel <- rbfdot(sigma = 0.1)
rbfkernel

kpar(rbfkernel)

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

## calculate dot product
rbfkernel(x,y)

# }


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