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Bi-Lipschitz Quotient embedding for Euclidean Group actions on Data
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For the action of the orthogonal group or euclidean group on k-tuples of vectors we construct a bi-Lipschitz embedding from the orbit space into euclidean space.This embedding has distortion sqrt(2).
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Cited by 3 Pith papers
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Coarea Reduction, Sparse Transfer, and Geometric Recomposition for Synchronized Singular Forms
For planar rotations, real phase retrieval, and finite reflection groups, linear transforms of max filter banks achieve distortion arbitrarily close to the Euclidean distortion of the orbit space.
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Recovering a group from few orbits
One generic complex orbit determines a finite linear symmetry group up to isomorphism; two generic real orbits suffice, and concrete recovery needs an orbit count governed by representation multiplicities.
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The generalized phase retrieval problem over compact groups
The paper frames multi-reference alignment and cryo-EM as generalized phase retrieval over compact groups and conjectures a bi-Lipschitz stability condition for recovery from the second moment.
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