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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2410.05446 |
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| _version_ | 1866909339852210176 |
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| author | Balan, Radu Tsoukanis, Efstratios Wellershoff, Matthias |
| author_facet | Balan, Radu Tsoukanis, Efstratios Wellershoff, Matthias |
| contents | Consider a group $G$ of order $M$ acting unitarily on a real inner product space $V$. We show that the sorting based embedding obtained by applying a general linear map $α: \mathbb{R}^{M \times N} \to \mathbb{R}^D$ to the invariant map $β_Φ: V \to \mathbb{R}^{M \times N}$ given by sorting the coorbits $(\langle v, g ϕ_i \rangle_V)_{g \in G}$, where $(ϕ_i)_{i=1}^N \in V$, satisfies a bi-Lipschitz condition if and only if it separates orbits.
Additionally, we note that any invariant Lipschitz continuous map (into a Hilbert space) factors through the sorting based embedding, and that any invariant continuous map (into a locally convex space) factors through the sorting based embedding as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05446 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of sorting based embeddings Balan, Radu Tsoukanis, Efstratios Wellershoff, Matthias Functional Analysis Machine Learning Consider a group $G$ of order $M$ acting unitarily on a real inner product space $V$. We show that the sorting based embedding obtained by applying a general linear map $α: \mathbb{R}^{M \times N} \to \mathbb{R}^D$ to the invariant map $β_Φ: V \to \mathbb{R}^{M \times N}$ given by sorting the coorbits $(\langle v, g ϕ_i \rangle_V)_{g \in G}$, where $(ϕ_i)_{i=1}^N \in V$, satisfies a bi-Lipschitz condition if and only if it separates orbits. Additionally, we note that any invariant Lipschitz continuous map (into a Hilbert space) factors through the sorting based embedding, and that any invariant continuous map (into a locally convex space) factors through the sorting based embedding as well. |
| title | Stability of sorting based embeddings |
| topic | Functional Analysis Machine Learning |
| url | https://arxiv.org/abs/2410.05446 |