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.
.
. 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.