Radial Basis Function

Radial Basis Function RBF is a radially symmetric scalar function, usually defined as a monotonic function of the distance from any point X in space to a center Xc, which can be recorded as K (|| X – Xc||). When X is far away from Xc, the function value is very small.

Radial Basis Function Application

Radial basis functions are mainly used to solve multivariate difference problems. A given number can be approximated by the sum of multiple radial basis functions. This approximation process can be regarded as a simple neural network.

In machine learning, radial basis functions are also used as kernel functions of support vector machines; in neural network structures, they can be used as the main functions of fully connected layers and ReLU layers.

Common radial basis functions

• Gaussian function
• Multi-quadratic function
• Inverse quadratic function
• Inverse multiquadratic function
• Polyharmonic splines
• Thin Plate Spline

Radial basis function applicable conditions

RBFs produce smooth surfaces based on a large number of data points; these functions produce good results for gently varying surfaces but are not suitable when the surface values vary dramatically over short distances or when the sample values may have measurement error or uncertainty.

An artificial neural network that uses radial basis function as the activation function is also called a radial basis function network.