Constructing a Station-Level Statistical Manifold with Dual Flat Structure from Pedestrian Trajectories

Note:I use AI assistance to draft and polish the English, but the analysis, interpretation, and core ideas are my own. Learning to write technical English is itself part of this project. Introduction In this article, I extend the pedestrian trajectory feature distributions measured in Article 3 to analyze pedestrian trajectory distributions across multiple urban locations. Rather than applying PCA, I construct a manifold where each location's distribution becomes a single coordinate point, and compute KL divergences based on dual flat structure for comparison between stations. By embedding each observation point's information onto the manifold, we can connect how differences in pedestrian behavioral dynamics are influenced by differences in urban spatial structure — a connection developed further in the next article. The key idea is to treat individual pedestrian trajectory observations not as isolated events, but as distributions where each observation point becomes a single point on