Page 20 - Rapid Learning in Robotics

6 Introduction

First, the importance and correctness of the learned prototypical asso-
ciation is clarified.

And second, the correct structural context is known.

This is important in order to draw meaningful inferences from the proto-
typical data set, when the system needs to generalize in new, previously
unknown situations.
The main focus of the present work are learning mechanisms of this
category: rapid learning – requiring only a small number of training data.
Our computational approach to the realization of such learning algorithm
is derived form the “Self-Organizing Map” (SOM). An essential new in-
gredient is the use of a continuous parametric representation that allows
a rapid and very flexible construction of manifolds with intrinsic dimen-

sionality up to 4 8 i.e. in a range that is very typical for many situations
in robotics.
This algorithm, is termed “Parameterized Self-Organizing Map” (PSOM)
and aims at continuous, smooth mappings in higher dimensional spaces.
The PSOM manifolds have a number of attractive properties.
We show that the PSOM is most useful in situations where the structure
of the obtained training data can be correctly inferred. Similar to the SOM,
the structure is encoded in the topological order of prototypical examples.
As explained in chapter 4, the discrete nature of the SOM is overcome by
using a set of basis functions. Together with a set of prototypical train-
ing data, they build a continuous mapping manifold, which can be used
in several ways. The PSOM manifold offers auto-association capability,
which can serve for completion of partial inputs and simultaneously map-
ping to multiple coordinate spaces.
The PSOM approach exhibits unusual mapping properties, which are
exposed in chapter 5. The special construction of the continuous manifold
deserves consideration and approaches to improve the mapping accuracy
and computational efficiency. Several extensions to the standard formu-
lations are presented in Chapter 6. They are illustrated at a number of
examples.
In cases where the topological structure of the training data is known
beforehand, e.g. generated by actively sampling the examples, the PSOM
“learning” time reduces to an immediate construction. This feature is of
particular interest in the domain of robotics: as already pointed out, here