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As at the RBF network case, the output of the network is a scalar function of the input vector, <math>\phi: \mathbb{R}^n\to\mathbb{R}</math>, is given by
<div style="text-align: center;"><math>\phi=\sum_{j=1}^{N}a_i\rho_j(||x-\mu_j||)</math></div>
Training HyperBF networks can be computationally challenging. Moreover, the high degree of freedom of HyperBF leads to overfitting and poor generalization. However, HyperBF networks have an important advantage that a small number of neurons is enough for learning complex functions.<ref name="Mahdi">R.N. Mahdi, E.C. Rouchka (2011). [http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=5733426 "Reduced HyperBF Networks: Regularization by Explicit Complexity Reduction and Scaled Rprop-Based Training"]. ''IEEE Transactions of Neural Networks'' '''2''':673–686.</ref>
==References==
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