Geographic Space as Manifolds
Hezhishi Jiang, Liyan Xu, Tianshu Li, Jintong Tang, Zekun Chen, Yuxuan, Wang, Hongmou Zhang, Yu Liu

TL;DR
This paper introduces the Geographic Manifold, a low-dimensional spatial representation capturing geographic constraints, which simplifies complex spatial analytics and is grounded in the intrinsic properties of geographic phenomena.
Contribution
It formally proves the existence of the Geographic Manifold and demonstrates its effectiveness in simplifying spatial analysis tasks.
Findings
Effective low-dimensional representation of geographic space.
Simplification of location choice and propagation analyses.
Grounded in intrinsic Euclidean properties of geographic phenomena.
Abstract
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…
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Taxonomy
TopicsHistorical Geography and Geographical Thought · Financial Crisis of the 21st Century · Historical Geography and Cartography
