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resolve the redundancies problem.
Despite the fact that the PSOM builds a global parametric model of the
map, it also bears the aspect of a local model, which maps each reference
point exactly (without any interferences by other training points, due to
the orthogonal set of basis functions).
The PSOM's character of being a local learning method can be gradu-
ally enhanced by applying the “Local-PSOMs” scheme. The L-PSOM algo-
rithm constructs the constant sized PSOM on a dynamically determined
sub-grid and keeps the computational effort constant when the number
of training points increases. Our results suggest an excellent cost–benefit
relation when using more than four nodes.
A further possibility to improve the mapping accuracy is the use of
“Chebyshev spaced PSOM”. The C-PSOM exploits the superior approxima-
tion capabilities of the Chebyshev polynomials for the design of the in-
ternal basis functions. When using four or more nodes per axis, the data
sampling and the associated node values are taken according to the distri-
bution of the Chebyshev polynomial's zeros. This imposes no extra effort
but offers a significant precision advantage.

A further main concern of this work is how to structure learning sys-
tems such that learning can be efficient. Here, we demonstrated a hier-
archical approach for context dependent learning. It is motivated by a
decomposition of the learning phase into two different stages: A longer, initial
“investment learning” phase “invests” effort in the collection of expertise in
prototypical context situations. In return, in the following “one-shot adapta-
tion” stage the system is able to extremely rapidly adapt to a new changing
context situation.
While PSOMs are very well suited for this approach, the underlying
idea to “compile” the effect of a longer learning phase into a one-step
learning architecture is more general and is independent of the PSOMs.
The META-BOX controls the parameterization of a set of context specific
“skills” which are implemented in a parameterized box - denoted T-BOX.
Iterative learning of a new context task is replaced by the dynamic re-para-
meterization through the META-BOX-mapping, dependent on the charac-
terizing observation of the context.
This emphasizes an important point for the construction of more pow-
erful learning systems: in addition to focusing on output value learning,