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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.14247 |
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| _version_ | 1866914967224057856 |
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| author | Diehl, Joscha Schmitz, Leonard |
| author_facet | Diehl, Joscha Schmitz, Leonard |
| contents | Quasisymmetric functions have recently been used in time series analysis as polynomial features that are invariant under, so-called, dynamic time warping. We extend this notion to data indexed by two parameters and thus provide warping invariants for images. We show that two-parameter quasisymmetric functions are complete in a certain sense, and provide a two-parameter quasi-shuffle identity. A compatible coproduct is based on diagonal concatenation of the input data, leading to a (weak) form of Chen's identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_14247 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Two-parameter sums signatures and corresponding quasisymmetric functions Diehl, Joscha Schmitz, Leonard Combinatorics Quasisymmetric functions have recently been used in time series analysis as polynomial features that are invariant under, so-called, dynamic time warping. We extend this notion to data indexed by two parameters and thus provide warping invariants for images. We show that two-parameter quasisymmetric functions are complete in a certain sense, and provide a two-parameter quasi-shuffle identity. A compatible coproduct is based on diagonal concatenation of the input data, leading to a (weak) form of Chen's identity. |
| title | Two-parameter sums signatures and corresponding quasisymmetric functions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2210.14247 |