Because of the special activation functions used for radial basis
functions, a special learning function is needed. It is impossible to
train networks which use the activation functions ` Act_``
RBF_` with backpropagation. The learning function for radial
basis functions implemented here can only be applied if the neurons
which use the special activation functions are forming the hidden
layer of a three layer feedforward network. Also the neurons of the
output layer have to pay attention to their bias for activation.

The name of the special learning function is `
RadialBasisLearning`. The required parameters are:

*(centers)*: the learning rate used for the modification of center vectors according to the formula .*(bias p)*: learning rate used for the modification of the parameters**p**of the base function.**p**is stored as bias of the hidden units and is trained by the following formula .*(weights)*: learning rate which influences the training of all link weights that are leading to the output layer as well as the bias of all output neurons.*delta max.*: To prevent an overtraining of the network the maximally tolerated error in an output unit can be defined. If the actual error is smaller than*delta max.*the corresponding weights are not changed. Common values range from 0 to .*momentum*: momentum term during training, after the formula . The momentum--term is usually chosen between and .

The learning rates to have to be selected very
carefully. If the values are chosen too large (like the size of
values for backpropagation) the modification of weights will be too
extensive and the learning function will become unstable. Tests
showed, that the learning procedure becomes more stable if only one of
the three learning rates is set to a value bigger than 0. Most
critical is the parameter * bias (p)*, because the base functions
are fundamentally changed by this parameter.

Tests also showed that the learning function working in batch mode is
much more stable than in online mode. Batch mode means that all
changes become active not before all learning patterns have been
presented once. This is also the training mode which is recommended in
the literature about radial basis functions. The opposite of batch
mode is known as online mode, where the weights are changed after the
presentation of every single teaching pattern. Which mode is to be
used can be defined during compilation of SNNS. The online mode is
activated by defining the C macro ` RBF_INCR_LEARNING` during
compilation of the simulator kernel, while batch mode is the default.

Niels.Mache@informatik.uni-stuttgart.de

Tue Nov 28 10:30:44 MET 1995