Radial Basis Function (RBF) kernel

The Radial Basis Function (RBF) kernel is a popular kernel function used in kernelized learning algorithms.

Operation

Computational methods

Programming Interface

dense

dense

compute(…)

compute_input

compute_result

Mathematical formulation

Computing

Given a set \(X\) of \(n\) feature vectors \(x_1 = (x_{11}, \ldots, x_{1p}), \ldots, x_n = (x_{n1}, \ldots, x_{np})\) of dimension \(p\) and a set \(Y\) of \(m\) feature vectors \(y_1 = (y_{11}, \ldots, y_{1p}), \ldots, y_m = (y_{m1}, \ldots, x_{mp})\), the problem is to compute the RBF kernel function \(K(x_i, y_i)\) for any pair of input vectors:

\[K\left({x}_{i},{y}_{j}\right)=exp\left(-\frac{{\left(\|{x}_{i}-{y}_{j}\|\right)}^{2}}{2{\sigma }^{2}}\right)\]

Computation method: dense

The method computes the rbf kernel function \(K(X, Y)\) for \(X\) and \(Y\) matrices.

Programming Interface

Refer to API Reference: Radial Basis Function (RBF) kernel.