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The presented potential field method was further applied to the kinematic arm model. Here, 150 eigenvectors were extracted (explaining 67.4% of the total variance), and the reduced set was used. The pattern association based on kernel PCA could learn the inverse onetomany mapping (table 5.3). However, the association with kernel PCA was worse than with the mixture of local PCA (the position errors were about double). The results were averaged over three separate training cycles. In the table, only averages are shown; the variation was small (for the kernel PCA method the maximum deviation of a position error from a mean value was 2 mm, and for the mixture of local PCA 5 mm).
On this task with fewer training patterns as in section 4.5, NGPCA was restricted to 100 units (in section 4.5, 200 units were used). Increasing this number diminished the performance.
Table 5.3:
Position and collision errors for an attractor network based on kernel PCA compared to one based on a mixture of local PCA (100 units, q = 6). Results are shown for two different directions of recall: forward and inverse. The inverse model takes the desired collision state as an additional input variable (third column). Position errors are averaged over 1331 test patterns, and are given with standard deviations. In the inverse case, the collision error is the percentage of trials deviating from the collision input value; in the forward case, it is the erroneous number of collision state predictions.
method 
direction 
input 
position error (mm) 
collision error (%) 
kernel PCA 
inverse 
no collision 
70 ± 33 
2.1 
kernel PCA 
inverse 
collision 
75 ± 40 
10.2 
kernel PCA 
forward 
 
150 ± 64 
20.5 
mixture of PCA 
inverse 
no collision 
40 ± 24 
7.7 
mixture of PCA 
inverse 
collision 
38 ± 27 
11.6 
mixture of PCA 
forward 
 
66 ± 46 
15.4 

Next: 5.4 Discussion
Up: 5.3.2 Results
Previous: 5.3.2.4 Recall on synthetic
Heiko Hoffmann
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