Scale Snapshot Topology Distance: Quantifying the Spatial Scale Effect From a Topological Perspective
Jiawei Zhu, Song Gao, Chao Tao, Yu Liu, Haifeng Li · Transactions in GIS · 2025
ABSTRACT Recognizing the degree of scale effect is crucial for selecting appropriate scales in spatial analyses. However, few methods are available for quantifying this effect. Topology, which studies invariants preserved under continuous deformation, provides an effective means of characterizing data. Therefore, we propose quantifying the scale effect by calculating the distance between topological invariants of data aggregated at different scales, termed the scale snapshot topology distance (SSTD). We summarize data snapshots aggregated at different scales using persistence diagrams, capturing essential information about topological invariants. We then quantify SSTD by computing the Wasserstein distance between these diagrams and apply it to track data variation across scale changes. Experiments on origin–destination data from five cities validate the effectiveness of the SSTD metric. Results demonstrate that our method identifies critical spatial scales near the consistency boundary of the scale effect, providing guidance for scale selection and showcasing the feasibility of topology‐based spatial data analysis.