Information Technology Reference
In-Depth Information
and heavy objects were fed consecutively into the network. On average it took less than
100 steps (about
200
ms
on a contemporary desktop computer) until the PB values con-
verged. The convergence criterion was set to 20 consecutive iterations where the cumu-
lative change of both PB values was
<
10
−
5
. To assure that the PB values reached a
stable state, this number has been successfully increased to 100,000 consecutive steps
in preliminary experiments (not shown). Note, that the network and PB values was not
reinitialized when the next sensory sequence was presented to the network. Thus, the
robot can continuously interact with the toy bricks and is able to immediately recognize
an object based on its sensorimotor sequence.
For testing, the network was operated in generalized recognition mode (Sec. 2.4).
Single trial bi-modal sensory sequences were presented to the network that in turn pro-
vided an 'identifying' PB value. The class membership, i.e. which object the robot holds
in its hand and how heavy this object is, was then determined based on the minimal Eu-
clidean distance to the PB values of the class prototypes (large symbols). In Fig. 6 the
PB values of all 80 single trial test patterns are depicted.
Only 4 out of 80 objects are misclassified (shown in gray), yielding an error rate
of 5 %. Interestingly, only star- and circular-shaped objects are confused by the net-
work, which indeed generate very similar sensory impressions (cf. Fig. 4). To assess
the meaning of the error rate and estimate how challenging the posed problem is, we
evaluated the data with two other commonly used techniques in machine learning. First,
we trained a multi-layer perceptron (28 input, 14 hidden and one output unit) with the
prototype sequences. Testing with the single trial data resulted in an error rate of 46.8 %,
reflecting weaker generalization capabilities of the non-recurrent architecture. Next, we
trained and evaluated our data with a support vector classifier (SVC) using default pa-
rameters [15]. In contrast, this method is able to classify the data perfectly.
4.3
Classification Using Only the Light Circular-Shaped and the Heavy
Triangular-Shaped Object for Training
In the second experiment, only the bi-modal prototypes for the light circular- and heavy
triangular-shaped objects were used to train the RNNPB. Although, the absolute PB
values obtained during training differ from the ones being determined in the previous
experiment, their relative Euclidean distance in PB space is nearly the same (1.39
vs.
1.35), stressing the data-driven self-organization of the parametric bias space.
For testing, initially only the bi-modal sensory time series matching the two training
conditions were fed into the network, thereby determining their PB values. Using the
Euclidean distance subsequently to obtain the class membership resulted in a flawless
identification of the two categories.
Further evaluation of the single trial test data was performed in two stages. In a primary
step the remaining test data was presented to the network and the respective PB values
were computed (generalized recognition, Sec. 2.4). Despite not having been trained with
prototypes for the remaining six object categories, the network is able to cluster PB values
stemming from similar sensory situations, i.e. identical object categories. In a succeeding
step we computed the centroid for each class (mean PB value) and classified again based
on the Euclidean distance. This time only two single trial time series were misclassified
by the network (error rate 2.5 %). The results are shown in Fig. 9.
