Bi-Lipschitz Quotient embedding for Euclidean Group actions on Data

Harm Derksen

Bi-Lipschitz Quotient embedding for Euclidean Group actions on Data

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arxiv 2409.06829 v1 pith:QEDUBSOG submitted 2024-09-10 math.AC math.MG

Harm Derksen This is my paper · ORCID

classification math.ACmath.MG

keywords embeddingeuclideangroupbi-lipschitzspaceactionactionsconstruct

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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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Coarea Reduction, Sparse Transfer, and Geometric Recomposition for Synchronized Singular Forms
math.FA 2026-03 accept novelty 7.0 of 10

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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