rbfkernel: Calculate RBF kernel matrix

Description Usage Arguments Details Value Author(s) See Also Examples

Description

Calculates the RBF kernel matrix for the dataset contained in the matrix X, where each row of X is a data point. If Y is also a matrix (with the same number of columns as X), the kernel function is evaluated between all data points of X and Y.

Usage

1
rbfkernel(X, sigma = 1, Y = NULL)

Arguments

X

matrix containing a data point in each row

sigma

kernel width of rbf kernel

Y

leave this NULL if the kernel function should be evaluated between the data points only contained in X (which can be regarded as Y = X) or to a matrix with same number of columns as X if you want to evaluate the function between the points of X and Y

Details

Each row of X must be a data point, i.e. X = (x_1, x_2, ..., x_n). The kernel matrix K is then defined as

K = (k(x_i, x_j)), i,j=1,...,n

If Y is not NULL and also contains data points in each row, i.e. Y = (y_1, y_2, ..., y_m), the kernel matrix K of X and Y is defined as

K = (k(x_i, x_j)), i=1,...,n, j=1,...,m

In this case, k is the rbf (radial basis function) kernel, which is defined as

k(x, y) = exp(-0.5*\|\|x - y\|\|\^2/sigma)

where x, y are data points and sigma is the rbf kernel width.

Value

RBF kernel matrix K for the given dataset

Author(s)

Jan Saputra Mueller

See Also

polykernel, sincdata

Examples

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## generate sinc data and calculate rbf kernel matrix with sigma = 1
d <- sincdata(100, noise = 0.1)
K <- rbfkernel(d$X)


rdetools documentation built on May 19, 2017, 7:08 p.m.
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