Radial basis function network: Difference between revisions

Revision as of 02:23, 6 August 2007

Revision as of 19:47, 23 August 2007

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:<math>\varphi(\mathbf{x}) = \sum_{i=1}^N a_i \rho(||\mathbf{x}-\mathbf{c}_i||)</math>

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 inputinputs 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>.