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DESCRIPTION: The Buchberger-Möller algorithm is a famous symbolic method fo
r finding all polynomials that vanish on a point cloud. It has even been ex
tended to noisy samples. However\, the resulting variety does not necessari
ly represent the topological or geometric structure of the data well. By ma
king use of the Vandermonde matrix\, it is possible to find polynomials of
a prescribed degree vanishing on the samples. As this matrix is severely il
l-conditioned\, modifications are necessary. By making use of statistical a
nd algebro-geometric techniques\, an algorithm for learning a vanishing ide
al that represents the data points‘ geometric properties well is presented.
It is investigated that this method -- among various other desirable prope
rties -- is more robust against perturbations in the data than the original
algorithm.
DTSTAMP:20201209T183700
DTSTART:20201214T140000
CLASS:PUBLIC
LOCATION:online
SEQUENCE:0
SUMMARY:Matthias Himmelmann: Generalized Principal Component Analysis for A
lgebraic Varieties
UID:107738951@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20201214-L-Himmelmann.html
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