Grassmann Clustering
Grassmann Clustering
Grassmann Clustering
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n(t)<br />
s(t) �<br />
A<br />
2.5<br />
2<br />
1.5<br />
1<br />
0.5<br />
0<br />
-0.5<br />
-1<br />
-1.5<br />
-2<br />
F. Theis<br />
x(t)<br />
V. Submanifold <strong>Clustering</strong><br />
Example<br />
-2.5<br />
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5<br />
data space<br />
44<br />
• use simple polynomial<br />
kernel k(x,y)=(x 2 ,y 2 ,2 -1/2 xy)<br />
• draw 100 hyperplanes<br />
samples from ellipses as<br />
shown<br />
• 3 samples per hyerplane<br />
• because in 4d - after<br />
affine embedding<br />
• convergence after 2 its<br />
• mismatch: 7 samples<br />
Apr 6, 2006 :: Tübingen
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