Radial basis function network: Difference between revisions

Revision as of 10:33, 19 October 2007

Revision as of 13:44, 25 October 2007

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:<math> \rho \big ( \left \Vert \mathbf{x} - \mathbf{c}_i \right \Vert \big ) = \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) = 0</math>

i.e. Changingchanging parameters of one neuron has only a small effect for input values that are far away from the center of that neuron.

RBF networks are [[universal approximator]]s on a compact subset of <math>\mathbb{R}^n</math>. This means that a RBF network with enough hidden neurons can approximate any continuous function with arbitrary precision.