Page 80 - Rapid Learning in Robotics

66 Characteristic Properties by Examples

Figure 5.4: Three examples of m dimensional manifolds M of a PSOM with
2 2 2 training vector points. They are shown as perspective surface plots of a
grid spanned by the eight corner reference vectors w a .

test grids the high-dimensional embedded manifolds can be visualized.
Selecting a good underlying node model is the first - and a very important
step. If a small training set is desired, the presented results suggest to start
with a PSOM with three nodes per axis. If one expects a linear dependence
in one degree of sampling, two nodes are sufficient.

5.2 Map Learning with Unregularly Sampled Train-
ing Points

Here, we want to explore the PSOM mapping behavior in case of the train-
ing samples not being drawn from an exact regular grid, but instead from
a “roughly regular” grid, sampled with some “jitter”. We consider the

example of a “barrel shaped” mapping IR IR , given by
x x x
(5.1)
x x
x x
s
x q

x x

Eq. 5.1 maps the unit cube [-1,1] into a barrel shaped region, shown in
Fig. 5.5. The first four plots in the upper row illustrate the mapping if the