ART2 Learning Function

For the ART2 learning function ART2 there are various parameters to specify. Here is a list of all parameters known from the theory:

 		 Vigilance parameter.  (first
parameter of the learning and update function).   is defined on
the interval  For some reason, described
in [Her92] only the following interval makes sense: 

a 		 Strength of the influence of the lower
level in F  by the middle level.  (second parameter of the learning
and update function).  Parameter a defines the importance of the
expection of F , propagated to F :  Normally a value of  is chosen to assure quick stabilization in
F .

b 		 Strength of the influence of the
middle level in F  by the upper level.  (third parameter of the
learning and update function).  For parameter b things are similar
to parameter a.  A high value for b is even more important,
because otherwise the network could become instable ([CG87b]).


c 		 Part of the length of vector  p
(units  p ...  p) used to compute the error.  (fourth
parameter of the learning and update function).  Choose c within 0
< c < 1.

d 		 Output value of the F  winner unit.
You won't have to pass d to  ART2, because this parameter is
already needed for initialization. So you have to enter the value,
when initializing the network (see subsection on the initialization
function).  Choose d within 0 < d < 1.  The parameters c and d
are dependent on each other.  For reasons of quick stabilization c
should be chosen as follows: .  On the other hand c
and d have to fit the following condition: 

e 		 Prevents from division by zero. Since
this parameter does not help to solve essential problems, it is
implemented as a fix value within the SNNS source code.

 		 Kind of threshold. For  the activation values of the units  x and
 q only have small influence (if any) on the middle level of F .
The output function f of the units  x and  q takes 
as its parameter. Since this noise function is continuously
differentiable, it is called  Out_ART2_Noise_ ContDiff in
SNNS.  Alternatively a piecewise linear output function may be used.
In SNNS the name of this function is  Out_ART2_Noise_PLin.
Choose  within 

To train an ART2 network, make sure, you have chosen the learning function ART2. As a first step initialize the network with the initialization function ART2_Weights described above. Then set the five parameters , a, b, c and , in the parameter windows 1 to 5 in both the LEARN and UPDATE lines of the remote panel. Example values are 0.9, 10.0, 10.0, 0.1, and 0.0. Then select the number of learning cycles, and finally use the buttons and to train a single pattern or all patterns at a time, respectively.