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construction of the desired manifold. This requires to assign the training
data set to the set of internal node locations. In other words, for this pro-
cedure the training data set must be known, or must be inferred (e.g. with
the SOM scheme).
The applicability is demonstrated in a number of examples employing
training data sets with the known topology of a multi-dimensional Carte-
sian grid. The resulting PSOM is immediately usable — without any need
for time consuming adaptation sequences. This feature is extremely ad-
vantageous in all cases where the training data can be sampled actively.
For example, in robotics, many sensorimotor transformations can be sam-
pled in a structured manner, without any additional cost.
Irrespectively of how the data model was initially generated the PSOM
can be fine-tuned on-line. Using the described error minimization proce-
dure, a PSOM can be refined even in the cases of coarsely sampled data,
when the original training data was corrupted by noise, or the underlying
task is changing. This is illustrated by the problem of adapting to sudden
changes in the robot's geometry and its corresponding kinematics.
The PSOM manifold is also called parameterized associative map since it
performs auto-associative completion of partial inputs. This facilitates multi-
directional mapping in contrast to only uni-directional feed-forward net-
works. Which components of the embedding space are selected as inputs,
is simply determined by specifying the diagonal elements p k of the projec-
tion matrix P. This mechanism allows to easily augment the embedding
space by further sub-spaces. As pointed out, the PSOM algorithm can
be implemented, such that inactive components do not affect the normal
PSOM operation.
Several examples demonstrate how to profitably utilize the multi-way
association capabilities: e.g. feature sets can be completed by a PSOM
in such a manner that they are invariant against certain operations (e.g.
shifted/rotated object) and provide at the same pass the unknown opera-
tion parameter (e.g. translation, angles).
The same mechanism offers a very natural and flexible way of sensor
data fusion. The incremental availability of more and more results from
different sensors can be used to improve the measurement accuracy and
confidence of recognition. Furthermore, the PSOM multi-way capability
enables an effective way of inter-sensor coordination and sensor system
guidance by predictions.