Tropical time series, iterated-sums signatures and quasisymmetric functions
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| Format: | Preprint |
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2020
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| _version_ | 1866914496482639872 |
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| author | Diehl, Joscha Ebrahimi-Fard, Kurusch Tapia, Nikolas |
| author_facet | Diehl, Joscha Ebrahimi-Fard, Kurusch Tapia, Nikolas |
| contents | Aiming for a systematic feature-extraction from time series, we introduce the iterated-sums signature over arbitrary commutative semirings. The case of the tropical semiring is a central, and our motivating example. It leads to features of (real-valued) time series that are not easily available using existing signature-type objects. We demonstrate how the signature extracts chronological aspects of a time series, and that its calculation is possible in linear time. We identify quasisymmetric expressions over semirings as the appropriate framework for iterated-sums signatures over semiring-valued time series. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2009_08443 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Tropical time series, iterated-sums signatures and quasisymmetric functions Diehl, Joscha Ebrahimi-Fard, Kurusch Tapia, Nikolas Rings and Algebras Computer Vision and Pattern Recognition Machine Learning 60L10, 60L70, 16Y60, 93C55 Aiming for a systematic feature-extraction from time series, we introduce the iterated-sums signature over arbitrary commutative semirings. The case of the tropical semiring is a central, and our motivating example. It leads to features of (real-valued) time series that are not easily available using existing signature-type objects. We demonstrate how the signature extracts chronological aspects of a time series, and that its calculation is possible in linear time. We identify quasisymmetric expressions over semirings as the appropriate framework for iterated-sums signatures over semiring-valued time series. |
| title | Tropical time series, iterated-sums signatures and quasisymmetric functions |
| topic | Rings and Algebras Computer Vision and Pattern Recognition Machine Learning 60L10, 60L70, 16Y60, 93C55 |
| url | https://arxiv.org/abs/2009.08443 |