kernlab (version 0.9-27)

dots: Kernel Functions


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.


rbfdot(sigma = 1)

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

tanhdot(scale = 1, offset = 1)


laplacedot(sigma = 1)

besseldot(sigma = 1, order = 1, degree = 1)

anovadot(sigma = 1, degree = 1)




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


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


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


The offset used in a polynomial or hyperbolic tangent kernel


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


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.


a list containing the kernel parameters (hyperparameters) used.

The kernel parameters can be accessed by the kpar function.


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.

See Also

stringdot, kernelMatrix , kernelMult, kernelPol


Run this code
rbfkernel <- rbfdot(sigma = 0.1)


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

## calculate dot product

# }

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