Trajectory analysis through entropy characterization over coded representation
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914786716942336 |
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| author | Peña-Mendieta, Roxana Mesa-Rodríguez, Ania Estevez-Rams, Ernesto Estevez-Moya, Daniel Kunka, Danays |
| author_facet | Peña-Mendieta, Roxana Mesa-Rodríguez, Ania Estevez-Rams, Ernesto Estevez-Moya, Daniel Kunka, Danays |
| contents | Any continuous curve in a higher dimensional space can be considered a trajectory that can be parameterized by a single variable, usually taken as time. It is well known that a continuous curve can have a fractional dimensionality, which can be estimated using already standard algorithms. However, characterizing a trajectory from an entropic perspective is far less developed. The search for such characterization leads us to use chain coding to discretize the description of a curve. Calculating the entropy density and entropy-related magnitudes from the resulting finite alphabet code becomes straightforward. In such a way, the entropy of a trajectory can be defined and used as an effective tool to assert creativity and pattern formation from a Shannon perspective. Applying the procedure to actual experimental physiological data and modelled trajectories of astronomical dynamics proved the robustness of the entropic characterization in a wealth of trajectories of different origins and the insight that can be gained from its use. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_03693 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Trajectory analysis through entropy characterization over coded representation Peña-Mendieta, Roxana Mesa-Rodríguez, Ania Estevez-Rams, Ernesto Estevez-Moya, Daniel Kunka, Danays Data Analysis, Statistics and Probability Information Theory Any continuous curve in a higher dimensional space can be considered a trajectory that can be parameterized by a single variable, usually taken as time. It is well known that a continuous curve can have a fractional dimensionality, which can be estimated using already standard algorithms. However, characterizing a trajectory from an entropic perspective is far less developed. The search for such characterization leads us to use chain coding to discretize the description of a curve. Calculating the entropy density and entropy-related magnitudes from the resulting finite alphabet code becomes straightforward. In such a way, the entropy of a trajectory can be defined and used as an effective tool to assert creativity and pattern formation from a Shannon perspective. Applying the procedure to actual experimental physiological data and modelled trajectories of astronomical dynamics proved the robustness of the entropic characterization in a wealth of trajectories of different origins and the insight that can be gained from its use. |
| title | Trajectory analysis through entropy characterization over coded representation |
| topic | Data Analysis, Statistics and Probability Information Theory |
| url | https://arxiv.org/abs/2405.03693 |