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132 “Mixture-of-Expertise” or “Investment Learning”

The solution ii represents the coordinate transformation as the prod-
uct of the four successive transformations. Thus, in this case the Meta-
PSOM controls the coefficients of a matrix multiplication. As in i , the
required parameter values are gained by a suitable calibration, or sys-
tem identification procedure.
When no explicit ansatz for the T-BOX is readily available, we can use
method iii . Here, for each prototypical context, the required T-mapping
is learned by a network and becomes encoded in its weight set . For this,
one can use any trainable network that meets the requirement stated at
the end of the previous section. However, PSOMs are a particularly con-
venient choice, since they can be directly constructed from a small data set
and additionally offer the advantage of associative multi-way mappings.
In this example, we chose for the T-BOX a2 2 2 “T-PSOM” that im-
plements the coordinate transform for both directions simultaneously. Its
training required eight training vectors arranged at the corners of a cubi-
cal grid, e.g. similar to the cube structure depicted in Fig. 7.2.
In order to compare approaches i iii , the transformation T-BOX
accuracy was averaged over a set of 50 contexts (given by 50 randomly
chosen object poses), each with 100 object volume points x to be trans-
formed into camera coordinates x .

T-BOX x - RMS [L] y - RMS [L] z - RMS [L]

(i) ( z ) 0.025 0.023 0.14
(ii) {A ij } 0.016 0.015 0.14
(iii) PSOM 0.015 0.014 0.12

Table 9.1: Results for the three variants in Fig. 9.5.

Comparing the RMS results in Tab. 9.1 shows, that the PSOM approach
(iii) can fully compete with the dedicated hand-crafted, one-way mapping
solutions (i) and (ii).

9.3.2 Rapid Visuo-motor Coordination Learning

The next example is concerned with a robot sensorimotor transformation.
It involves the Puma robot manipulator, which is monitored by a camera,
see Fig. 9.6. The robot is positioned behind a table and the entire scene is