kerntools (version 1.2.0)

RBF: Gaussian RBF (Radial Basis Function) kernel

Description

`RBF()` computes the RBF kernel between all possible pairs of rows of a matrix or data.frame with dimension NxD.

Usage

RBF(X, g = NULL)

Value

Kernel matrix (dimension: NxN).

Arguments

X

Matrix or data.frame that contains real numbers ("integer", "float" or "double").

g

Gamma hyperparameter. If g=0 or NULL, `RBF()` returns the matrix of squared Euclidean distances instead of the RBF kernel matrix. (Defaults=NULL).

Details

Let \(x_i,x_j\) be two real vectors. Then, the RBF kernel is defined as: $$K_{RBF}(x_i,x_j)=\exp(-\gamma \|x_i - x_j \|^2)$$

Sometimes the RBF kernel is given a hyperparameter called sigma. In that case: \(\gamma = 1/\sigma^2\).

Examples

dat <- matrix(rnorm(250),ncol=50,nrow=5)
RBF(dat,g=0.1)