Defining the urban "local" with low dimensional manifolds of human mobility networks

2025-10-20

AI Summary

Existing urban science research overlooks the local heterogeneity of human mobility networks, rendering fine-grained urban regional characteristics invisible. To address this, we propose a novel framework integrating topological data analysis and manifold learning, which— for the first time—formalizes “mobility locality” as a geometric entity embedded in a low-dimensional manifold (≤5D), yielding a compact and interpretable geometric representation of urban space. Our method synergistically combines network science with geographic embedding to automatically identify locally coherent regions that exhibit high spatial congruence with official administrative boundaries. Empirical evaluation demonstrates substantial improvements in both accuracy and scalability for facility location optimization and epidemic/behavioral diffusion modeling. By unifying global generalizability with local specificity, our approach establishes a new paradigm for urban science grounded in geometric, topology-aware, and geographically meaningful representations.

Technology Category

• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Local Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Web Mining and Content Analysis: Machine learning and data science for the Web

Abstract

Urban science has largely relied on universal models, rendering the heterogeneous and locally specific nature of cities effectively invisible. Here we introduce a topological framework that defines and detects localities in human mobility networks. We empirically demonstrate that these human mobility network localities are rigorous geometric entities that map directly to geographic localities, revealing that human mobility networks lie on manifolds of dimension <=5. This representation provides a compact theoretical foundation for spatial embedding and enables efficient applications to facility location and propagation modeling. Our approach reconciles local heterogeneity with universal representation, offering a new pathway toward a more comprehensive urban science.

Problem

• Defining urban localities using low-dimensional mobility manifolds
• Detecting geometric structures in human mobility networks
• Reconciling local heterogeneity with universal urban representation

Innovation

• Topological framework defines human mobility localities
• Manifolds of dimension <=5 represent mobility networks
• Compact spatial embedding enables efficient urban applications