C++ Neural Networks and Fuzzy Logic: Preface

Radial Basis−Function Networks

Although details of radial basis functions are beyond the scope of this book, it is worthwhile to contrast the

learning characteristics for this type of neural network model. Radial basis−function networks in topology

look similar to feedforward networks. Each neuron has an output to input characteristic that resembles a radial

function (for two inputs, and thus two dimensions). Specifically, the output h(x) is as follows:

h(x)  = exp [ (x − u)

2

 / 2[sigma]

2

   ]

C++ Neural Networks and Fuzzy Logic:Preface

Statistical Training and Simulated Annealing

104

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Here, x is the input vector, u is the mean, and [sigma] is the standard deviation of the output response curve of

the neuron. Radial basis function (RBF) networks have rapid training time (orders of magnitude faster than

backpropagation) and do not have problems with local minima as backpropagation does. RBF networks are

used with supervised training, and typically only the output layer is trained. Once training is completed, a

RBF network may be slower to use than a feedforward Backpropagation network, since more computations

are required to arrive at an output.

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C++ Neural Networks and Fuzzy Logic:Preface

Statistical Training and Simulated Annealing

105

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