Bi-Lipschitz Quotient embedding for Euclidean Group actions on Data

TL;DR

This paper introduces a bi-Lipschitz embedding for the orbit space of Euclidean group actions on vector k-tuples, achieving low distortion and enabling better geometric understanding of data transformations.

Contribution

The paper constructs a novel bi-Lipschitz embedding with minimal distortion for Euclidean group actions, improving geometric analysis of data under group symmetries.

Findings

Embedding has distortion sqrt(2)

Orbit space can be embedded into Euclidean space

Enhances geometric analysis of symmetric data

Abstract

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).