| Autor: |
Sabol, John, Barnhill, David, Yoshida, Ruriko, Miura, Keiji |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We study the geometry of tropical Fermat-Weber points in terms of the symmetric tropical metric over the tropical projective torus. It is well-known that a tropical Fermat-Weber point of a given sample is not unique and we show that the set of all possible Fermat-Weber points forms a polytrope. To prove this, we show that the tropical Fermat-Weber polytrope is a bounded cell of a tropical hyperplane arrangement given by both max- and min-tropical hyperplanes with apices given by the sample. We also define tropical Fermat-Weber gradients and provide a gradient descent algorithm that converges to the Fermat-Weber polytrope. |
| Databáze: |
arXiv |
| Externí odkaz: |
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