Quantifying displacement: a gentrification's consequence via persistent homology

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.