Radial Basis Function Network

A radial basis function (RBF) network is a type of neural network used for classification tasks.

RBF networks are used when the problem domain provides known centers and deviations for the hidden layer neurons. They are particularly effective for multiclass classification with many potential classes.

An RBF network consists of three layers: an input layer, a hidden layer with radial basis function neurons, and an output layer. The input layer accepts a vector of values. The hidden layer neurons use a Gaussian function to measure deviations from their centers and propagate these deviations to the output layer. A “center” in this context refers to a specific point in the input space around which the Gaussian function is centered. The output layer neurons represent classifications and are activated based on the probability that the input data fits their classification.

For example, in a trained RBF network, each output neuron will be activated depending on the probability with which the data supplied to the input layer fits its classification.

RBF networks can learn any classification with just one hidden layer by adding multiple Gaussian functions. However, the challenge lies in determining the right centers and deviations for the hidden layer neurons. Variants of RBF networks can learn these values and the weights connecting the hidden layer to the output layer. RBF networks are preferable when the centers and deviations are known, while perceptrons are better when they are not.

In summary, RBF networks are crucial for classification tasks with known centers and deviations, and they train better than perceptrons when there are many output neurons.