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4.4 Learning Phases 53

or one out of several local minima as best-match is discussed in section 6.1.

4.4 Learning Phases

As pointed out in the introduction, in the biological world we find many
types of learning. The PSOM approach offers several forms by itself.
One PSOM's core idea is the construction of the continuous mapping
manifold using a topologically ordered set of reference vectors w s. There-
fore the first question of learning can be formulated: how to obtain the
topological order of the reference vectors w a? The second question is,
how to adapt and improve the mapping accuracy in an on-line fashion,
allowing to cope with drifting and changing tasks and target mappings?
The PSOM algorithm offers two principal ways for this initial learning
phase:

PSOM Unsupervised Self-Organization Mode: One way is to employ the
Kohonen adaptation rule Eq. 3.10 described in Sect. 3.7. The ad-
vantage is that no structural information is required. On the other
hand this process is iterative and can be slow. It might require much
more data to recover the correct structural order (see also stimulus-
sampling theory in the introduction). Numerous examples on the
self-organizing process are given in the literature, e.g. (Kohonen 1990;
Ritter, Martinetz, and Schulten 1992; Kohonen 1995))

PSOM Supervised Construction (PAM: Parameterized Associative Map)
In some cases, the information on the topological order of the train-
ing data set can be otherwise inferred — for example generated — by ac-
tively sampling the training data. In the robotics domain frequently
this can be done by structuring the data gathering process — often
without any extra effort.

Then the learning of the PSOM is sped up tremendously: the iterative
self-organization step can be replaced by an immediate construction.
The prototypically sampled data vectors w a are simply assigned to
the node locations a in the set A. In the following chapter, several
examples shall illustrate this procedure.
Irrespective of the way in which the initial structure of the PSOM map-
ping manifold was established, the PSOM can be continuously fine-tuned