Radial basis function network: Difference between revisions

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Network architecture: c_i -> \mathbf c_i
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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>\mathbf 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 ) = \exp \left[ -\beta \left \Vert \mathbf{x} - \mathbf{c}_i \right \Vert ^2 \right] </math>.