Population displacement is a housing-related involuntary residential dislocation. It has become increasingly widespread in many cities, particularly in neighbourhoods undergoing rapid economic and demographic change, and measuring it is essential to assess the social consequences of urban transformation and housing market pressures. Despite its relevance, quantifying displacement presents difficulties due to limited replicability across cities and time periods and the need to analyse long time spans: displacement is a gradual process, impossible to capture in one data snapshot. We introduce a novel tool to overcome these difficulties. Using publicly available address change data, we construct four cubical complexes simultaneously incorporating geographical and temporal information of people moving, and analyse using Topological Data Analysis tools. Finally, we demonstrate this method through a 20-year case study in Madrid, Spain. The results reveal its ability to capture displacement and identify the neighbourhoods and years affected--patterns not observable from raw address change data.

翻译：人口迁移是一种与住房相关的非自愿居住地变更。这一现象在众多城市中日益普遍，尤其在经历快速经济与人口变化的社区尤为显著。对其的量化评估是衡量城市转型与社会住房市场压力的关键。尽管意义重大，但由于跨城市与跨时段的可重复性受限，加之需要分析长期跨度——迁移作为渐进过程无法通过单次数据快照捕捉，量化迁移面临诸多困难。我们提出一种创新工具应对这些挑战。通过利用公开的地址变更数据，我们构建四个同时融合人口迁移时空信息的立方体复合形，并采用拓扑数据分析工具进行分析。最终以西班牙马德里20年案例研究验证该方法。结果显示，该方法能够有效捕捉迁移现象并识别受影响的社区与年份——这些模式在原始地址变更数据中无法直接观测。