Radial basis function network: Difference between revisions

Revision as of 08:57, 10 October 2007

Revision as of 10:59, 12 October 2007

Line 11:

where ''N'' is the number of neurons in the hidden layer, <math>c_i</math> is the center vector for neuron ''i'', and <math>a_i</math> are the weights of the linear output neuron. In the basic form all inputs are connected to each hidden neuron. The norm is typically taken to be the [[Euclidean distance]] and the basis function is taken to be [[Normal distribution|Gaussian]]

:<math> \rho \big ( \left \Vert \mathbf{x} - \mathbf{c}_i \right \Vert \big ) \propto= \exp \left[ -\beta \left \Vert \mathbf{x} - \mathbf{c}_i \right \Vert ^2 \right] </math>.

The Gaussian basis functions are local in the sense that <math>\lim_{||x|| \to \infty}\rho(\left \Vert \mathbf{x} - \mathbf{c}_i \right \Vert)</math>. Changing parameters of one neuron has only a small effect for input values that are far away from the center of that neuron.