Radial Basis Function

Radial Basis Function

A radial basis function (RBF) is a real-valued function whose value depends only on the distance from the origin, so that ; or alternatively on the distance from some other point c, called a center, so that . Any function that satisfies the property is a radial function. The norm is usually Euclidean distance, although other distance functions are also possible. For example by using Lukaszyk-Karmowski metric, it is possible for some radial functions to avoid problems with ill conditioning of the matrix solved to determine coefficients w_i (see below), since the is always greater than zero.

Sums of radial basis functions are typically used to approximate given functions. This approximation process can also be interpreted as a simple kind of neural network.