Radial Basis Function Network

Introduction

A RBF Network is a type of artificial neural network that uses radial basis functions as activation functions. It is a linear combination of radial basis functions. They are used in function approximation, time series prediction, and control.

Structure

In its simplest form, an RBF network is a three-layer feedforward artificial neural network. The layers are typically referred to as the input layer, the hidden layer, and the output layer.

Input Layer

The input layer of an RBF network consists of source nodes. These nodes are responsible for interfacing with the actual inputs to the network. Each node in the input layer corresponds to a different element or feature of the input vector.

Hidden Layer

The hidden layer of an RBF network is composed of a set of "neurons" or "nodes". Each node in the hidden layer applies a non-linear transformation to the weighted inputs it receives from the input layer. This transformation is typically a Gaussian function, but can also be a multiquadric or inverse multiquadric function.

Output Layer

The output layer of an RBF network is a linear combination of the outputs from the hidden layer. Each node in the output layer corresponds to a different class or output of the network.

Radial Basis Functions

The radial basis functions used in an RBF network are typically Gaussian functions, but can also be multiquadric or inverse multiquadric functions. The choice of radial basis function can have a significant impact on the performance of the network.

Training an RBF Network

Training an RBF network typically involves two steps: determining the parameters of the radial basis functions in the hidden layer, and determining the weights of the linear combination in the output layer.

Applications of RBF Networks

RBF networks are used in a wide variety of applications, including function approximation, time series prediction, and control. They are particularly well-suited to problems where the relationship between the input and output variables is complex and non-linear.