Estimating the Euclidean distortion of an orbit space
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908394248470528 |
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| author | Blum-Smith, Ben Derksen, Harm Mixon, Dustin G. Qaddura, Yousef Vose, Brantley |
| author_facet | Blum-Smith, Ben Derksen, Harm Mixon, Dustin G. Qaddura, Yousef Vose, Brantley |
| contents | Given a finite-dimensional inner product space $V$ and a group $G$ of isometries, we consider the problem of embedding the orbit space $V/G$ into a Hilbert space in a way that preserves the quotient metric as well as possible. This inquiry is motivated by applications to invariant machine learning. We introduce several new theoretical tools before using them to tackle various fundamental instances of this problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04425 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimating the Euclidean distortion of an orbit space Blum-Smith, Ben Derksen, Harm Mixon, Dustin G. Qaddura, Yousef Vose, Brantley Metric Geometry Information Theory Functional Analysis Representation Theory Given a finite-dimensional inner product space $V$ and a group $G$ of isometries, we consider the problem of embedding the orbit space $V/G$ into a Hilbert space in a way that preserves the quotient metric as well as possible. This inquiry is motivated by applications to invariant machine learning. We introduce several new theoretical tools before using them to tackle various fundamental instances of this problem. |
| title | Estimating the Euclidean distortion of an orbit space |
| topic | Metric Geometry Information Theory Functional Analysis Representation Theory |
| url | https://arxiv.org/abs/2506.04425 |