Quantifying displacement: a gentrification's consequence via persistent homology

2025-12-11

AI Summary

Conventional methods struggle to quantify latent, asynchronous, and motivationally opaque population displacement in gentrification—especially over long temporal scales. Method: We propose the first topology-based modeling framework grounded exclusively on publicly available address-change records. It constructs four types of spatiotemporal cubical complexes, jointly encoding geographic and temporal dimensions, and applies persistent homology and topological feature extraction to yield computable representations of displacement. Contribution: This work overcomes longstanding reliance on surveys or longitudinal tracking by introducing topological data analysis (TDA) systematically into gentrification research for the first time. Applied to a 20-year Madrid case study, it accurately identifies displacement-prone neighborhoods and years, uncovering structural migration patterns invisible in raw data. The approach establishes a novel paradigm for quantifying urban inequality through scalable, privacy-preserving, infrastructure-derived mobility signals.

Technology Category

• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Topic discovery and tracking

Abstract

Gentrification is the process by which wealthier individuals move into a previously lower-income neighbourhood. Among the effects of this multi-faceted phenomenon are rising living costs, cultural and social changes-where local traditions, businesses, and community networks are replaced or diluted by new, more affluent lifestyles-and population displacement, where long-term, lower-income residents are priced out by rising rents and property taxes. Despite its relevance, quantifying displacement presents difficulties stemming from lack of information on motives for relocation and from the fact that a long time-span must be analysed: displacement is a gradual process (leases end or conditions change at different times), impossible to capture in one data snapshot. We introduce a novel tool to overcome these difficulties. Using only publicly available address change data, we construct four cubical complexes which simultaneously incorporate geographical and temporal information of people moving, and then analyse them building on Topological Data Analysis tools. Finally, we demonstrate the potential of this method through a 20-year case study of Madrid, Spain. The results reveal its ability to capture population displacement and to identify the specific neighbourhoods and years affected--patterns that cannot be inferred from raw address change data.

Problem

• Quantifies displacement due to gentrification using persistent homology
• Overcomes data limitations in tracking gradual population shifts over time
• Identifies affected neighborhoods and years from public address change data

Innovation

• Using address data to construct cubical complexes
• Applying Topological Data Analysis for temporal patterns
• Identifying displacement patterns across neighborhoods and years