Sasaki Metric for Spline Models of Manifold-Valued Trajectories
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929251908845568 |
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| author | Nava-Yazdani, Esfandiar Ambellan, Felix Hanik, Martin von Tycowicz, Christoph |
| author_facet | Nava-Yazdani, Esfandiar Ambellan, Felix Hanik, Martin von Tycowicz, Christoph |
| contents | We propose a generic spatiotemporal framework to analyze manifold-valued measurements, which allows for employing an intrinsic and computationally efficient Riemannian hierarchical model. Particularly, utilizing regression, we represent discrete trajectories in a Riemannian manifold by composite B\' ezier splines, propose a natural metric induced by the Sasaki metric to compare the trajectories, and estimate average trajectories as group-wise trends. We evaluate our framework in comparison to state-of-the-art methods within qualitative and quantitative experiments on hurricane tracks. Notably, our results demonstrate the superiority of spline-based approaches for an intensity classification of the tracks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17299 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sasaki Metric for Spline Models of Manifold-Valued Trajectories Nava-Yazdani, Esfandiar Ambellan, Felix Hanik, Martin von Tycowicz, Christoph Differential Geometry Machine Learning Applications 53Zxxx We propose a generic spatiotemporal framework to analyze manifold-valued measurements, which allows for employing an intrinsic and computationally efficient Riemannian hierarchical model. Particularly, utilizing regression, we represent discrete trajectories in a Riemannian manifold by composite B\' ezier splines, propose a natural metric induced by the Sasaki metric to compare the trajectories, and estimate average trajectories as group-wise trends. We evaluate our framework in comparison to state-of-the-art methods within qualitative and quantitative experiments on hurricane tracks. Notably, our results demonstrate the superiority of spline-based approaches for an intensity classification of the tracks. |
| title | Sasaki Metric for Spline Models of Manifold-Valued Trajectories |
| topic | Differential Geometry Machine Learning Applications 53Zxxx |
| url | https://arxiv.org/abs/2303.17299 |