Injectivity, stability, and positive definiteness of max filtering
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916704128335872 |
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| author | Mixon, Dustin G. Qaddura, Yousef |
| author_facet | Mixon, Dustin G. Qaddura, Yousef |
| contents | Given a real inner product space V and a group G of linear isometries, max filtering offers a rich class of G-invariant maps. In this paper, we identify nearly sharp conditions under which these maps injectively embed the orbit space V/G into Euclidean space, and when G is finite, we estimate the map's distortion of the quotient metric. We also characterize when max filtering is a positive definite kernel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11156 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Injectivity, stability, and positive definiteness of max filtering Mixon, Dustin G. Qaddura, Yousef Functional Analysis Information Theory Given a real inner product space V and a group G of linear isometries, max filtering offers a rich class of G-invariant maps. In this paper, we identify nearly sharp conditions under which these maps injectively embed the orbit space V/G into Euclidean space, and when G is finite, we estimate the map's distortion of the quotient metric. We also characterize when max filtering is a positive definite kernel. |
| title | Injectivity, stability, and positive definiteness of max filtering |
| topic | Functional Analysis Information Theory |
| url | https://arxiv.org/abs/2212.11156 |