Grassmann Clustering
Grassmann Clustering
Grassmann Clustering
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n(t)<br />
s(t) �<br />
A<br />
F. Theis<br />
x(t)<br />
IV. <strong>Grassmann</strong> <strong>Clustering</strong><br />
Application to NMF<br />
• Nonnegative Matrix Factorization<br />
• observing X=AS+N with everything with nonneg.<br />
coefficients, find unknown A and S<br />
• key idea:<br />
• X is conic hull with edges given by columns of A<br />
• projection onto std simplex yields:<br />
• X‘ lies in the convex hull with vertices given by A<br />
• example:<br />
• n=3, 100 uniform samples<br />
34<br />
Apr 6, 2006 :: Tübingen
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