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Next: Recall on synthetic Up: 5.3.2 Results Previous: Dependence on the Speed-up

Using the speed-up, for the ring-line-square distribution, the potential field based on the reduced set was only sightly impaired (quality: 92.5% compared to 93.7%, compare also figure 5.5 with 5.3). On the vortex distribution, the region surrounded by the iso-potential curve enclosing the same volume as the distribution shows holes (figure 5.5). However, the approximation is still reasonably good (quality: 85.0% compared to 95.0%).

Figure: Iso-potential curves in the original space of a cylindrical potential field with 40 principal components in feature space. Here, the speed-up as described in section B.2 was used. The right pictures show the iso-potential curve enclosing an area of same size as the distribution (above covering 92.5% and below covering 85.0% of the data points).
\includegraphics[height=3cm,width=6.5cm]{kpca/ringsquare40evSig0.3Burges85contour.eps} \includegraphics[height=3cm,width=6.5cm]{kpca/ringsquare40evSig0.3Burges85sameVol.eps}

\includegraphics[height=6.2cm,width=6.5cm]{kpca/vortex40evSig0.3Burges70contour.eps} \includegraphics[height=6.2cm,width=6.5cm]{kpca/vortex40evSig0.3Burges70sameVol.eps}

Heiko Hoffmann