Grassmann Clustering

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n(t) s(t) � A F. Theis x(t) IV. Grassmann Clustering Polytope identification • solve approximation problem (from comp. geometry) • given set of points, identify smallest enclosing convex polytope with fixed number of faces k • algorithm: • compute convex hull (QHull) • apply subspace k-means to faces • note: affine version nec. • include sample weighting by volume • possibly intersect resulting clusters 33 Apr 6, 2006 :: Tübingen
n(t) s(t) � A F. Theis x(t) IV. Grassmann Clustering Application to NMF • Nonnegative Matrix Factorization • observing X=AS+N with everything with nonneg. coefficients, find unknown A and S • key idea: • X is conic hull with edges given by columns of A • projection onto std simplex yields: • X‘ lies in the convex hull with vertices given by A • example: • n=3, 100 uniform samples 34 Apr 6, 2006 :: Tübingen
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n(t) s(t) � A x(t) Grassmann Clus
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n(t) s(t) � A F. Theis x(t) I. In
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Grassmann Clustering

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