# Kernel functions

### Description

Compute similarities between feature vectors according to a specific kernel function

### Usage

1 2 3 4 5 6 7 | ```
cauchy.kernel(W, sigma = 1)
laplacian.kernel(W, sigma = 1)
gaussian.kernel(W, sigma = 1)
inv.multiquadric.kernel(W, v = 1)
identity.kernel(W, a = 1)
linear.kernel(W, a = 1)
poly.kernel(W, degree = 2, scale = -1, v = 0)
``` |

### Arguments

`W` |
a numeric matrix, Rows are examples and columns are features |

`sigma` |
a real value representing the sigma parameter (def. 1) of the Cauchy, Gaussian and Laplacian kernel |

`v` |
constant factor (def. 1) of the inverse multiquadric kernel and of the polynomail kernel; for the inverse multiquadric kernel v must be larger than 0. |

`a` |
unused parameter, maintained for compatibility reasons . |

`degree` |
integer corresponding to a degree of the polynomial (def. 2) |

`scale` |
double: scaling factor of the polynomial kernel. If |

### Details

All the kernel matrices are computed by calling C code to speed-up the computation.

`cauchy.kernel`

computes the Cauchy kernel.

`laplacian.kernel`

computes the Lapalacian kernel.

`gaussian.kernel`

computes the Gaussian kernel.

`inv.multiquadric.kernel`

computes the inverse multiquadric kernel.

`identity.kernel`

computes the identity kernel. In this case the input W represents a similarity square matrix (obtained i.e. through the Pearson correlation) between examples.

`linear.kernel`

computes the linear kernel.

### Value

A kernel matrix representing the similarities between the examples (rows of W), according to a specific kernel function.

### See Also

`rw.kernel-methods`

### Examples

1 2 3 4 5 6 7 8 9 10 11 | ```
# computing kernels on the Tanimoto chemical structure similarity matrix
library(bionetdata);
data(DD.chem.data);
K <- identity.kernel(DD.chem.data);
K <- linear.kernel(DD.chem.data);
## Not run:
K <- gaussian.kernel(DD.chem.data);
K <- inv.multiquadric.kernel(DD.chem.data);
K <- poly.kernel(DD.chem.data);
## End(Not run)
``` |