Geographic Space as Manifolds
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912135908425728 |
|---|---|
| author | Jiang, Hezhishi Xu, Liyan Li, Tianshu Tang, Jintong Chen, Zekun Wang, Yuxuan Zhang, Hongmou Liu, Yu |
| author_facet | Jiang, Hezhishi Xu, Liyan Li, Tianshu Tang, Jintong Chen, Zekun Wang, Yuxuan Zhang, Hongmou Liu, Yu |
| contents | The communications and interrelations between different locations on the Earth's surface have far-reaching implications for both social and natural systems. Effective spatial analytics ideally require a spatial representation, where geographic principles are succinctly expressed within a defined metric space. However, common spatial representations, including map-based or network-based approaches, fall short by incompletely or inaccurately defining this metric space. Here we show, by introducing an inverse friction factor that captures the spatial constraints in spatial networks, that a homogeneous, low-dimensional spatial representation - termed the Geographic Manifold - can be achieved. We illustrate the effectiveness of the Geographic Manifold in two classic scenarios of spatial analytics - location choice and propagation, where the otherwise complicated analyses are reduced to straightforward regular partitioning and concentric diffusing, respectively on the manifold with a high degree of accuracy. We further empirically explain and formally prove the general existence of the Geographic Manifold, which is grounded in the intrinsic Euclidean low-dimensional statistical physics properties of geographic phenomena. This work represents a step towards formalizing Tobler's famous First Law of Geography from a geometric approach, where a regularized geospace thereby yielded is expected to contribute in learning abstract spatial structure representations for understanding and optimization purposes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23559 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geographic Space as Manifolds Jiang, Hezhishi Xu, Liyan Li, Tianshu Tang, Jintong Chen, Zekun Wang, Yuxuan Zhang, Hongmou Liu, Yu Physics and Society The communications and interrelations between different locations on the Earth's surface have far-reaching implications for both social and natural systems. Effective spatial analytics ideally require a spatial representation, where geographic principles are succinctly expressed within a defined metric space. However, common spatial representations, including map-based or network-based approaches, fall short by incompletely or inaccurately defining this metric space. Here we show, by introducing an inverse friction factor that captures the spatial constraints in spatial networks, that a homogeneous, low-dimensional spatial representation - termed the Geographic Manifold - can be achieved. We illustrate the effectiveness of the Geographic Manifold in two classic scenarios of spatial analytics - location choice and propagation, where the otherwise complicated analyses are reduced to straightforward regular partitioning and concentric diffusing, respectively on the manifold with a high degree of accuracy. We further empirically explain and formally prove the general existence of the Geographic Manifold, which is grounded in the intrinsic Euclidean low-dimensional statistical physics properties of geographic phenomena. This work represents a step towards formalizing Tobler's famous First Law of Geography from a geometric approach, where a regularized geospace thereby yielded is expected to contribute in learning abstract spatial structure representations for understanding and optimization purposes. |
| title | Geographic Space as Manifolds |
| topic | Physics and Society |
| url | https://arxiv.org/abs/2410.23559 |