The initialization function CPN_Weights is used for
Counterpropagation. Two parameters are used which represent the
minimum (a) and maximum (b) of the range out of which initial
values for the second (Grossberg) layer are selected at random. The
vector 
of weights leading to unit i of the Kohonen layer are
initialized as normalized vectors (length 1) drawn at random from part
of a hyper-sphere. Here, min and max determine which part of the
hyper-sphere is used according to table 
.
Table: Influence of minimum and maximum on the initialization of weight
vectors for CPN and SOM.
Note:
This function has been changed in SNNSv3.3. The earlier
counterpropagation initialization function generated initial random
points in a rectangular region in space (usually from the hypercube
if the default parameter settings were used) and
normalized these vectors to unit length. This resulted in an uneven
distribution density on the unit sphere, because the diagonal of the
unit hypercube is longer than 1. It also yielded non-obvious results
if non-standard parameter values, (e.g. [1, 2]) were chosen. The new
method eliminates these drawbacks by dropping initial points outside
the hyper-sphere (see fig. (left) for the 2D case and
fig. (right) for the 3D case).
Figure: Choosing random initialization points from a sector of a
circle or from the full circle (left side); choosing initialization
points from a sector of a (hyper)sphere or a full (hyper)sphere (right
side)