Radial basis function network: Difference between revisions

Revision as of 22:25, 9 July 2007

Revision as of 18:04, 17 July 2007

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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.

RBF networks are [[universal approximatorsapproximator]]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.

The weights <math> a_i </math>, <math> \mathbf{c}_i </math>, and <math> \beta </math> are determined in a manner that optimizes the fit between <math> \varphi </math> and the data.