📝 Original Info
- Title: Quantifying displacement: a gentrifications consequence via persistent homology
- ArXiv ID: 2512.10753
- Date: 2025-12-11
- Authors: Researchers from original ArXiv paper
📝 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.
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Deep Dive into Quantifying displacement: a gentrifications 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 mo
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QUANTIFYING DISPLACEMENT: A GENTRIFICATION’S CONSEQUENCE
VIA PERSISTENT HOMOLOGY
RITA RODR´IGUEZ V´AZQUEZ1 AND MANUEL CUERNO2, A
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 snap-
shot. 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.
1. Introduction
Population displacement, a housing-related involuntary residential dislocation [34] is one of the
main symptoms of gentrification. Ruth Glass, who coined the term gentrification in her 1964 book
“London: Aspects of Change” [28], already observed that gentrification was pushing lower income
people and small businesses away from their original locations. The widespread and uneven effect of
displacement across social groups has motivated a broad range of studies, focussing on everything
from characterising displaced individuals to identifying the potential causes and consequences of
the phenomenon.
A wide range of approaches has been employed to assess the extent of displacement in gentrifying
areas. Survey-supported research detects displacement by explicitly inquiring about individuals’
motivations for relocation. The seminal 1981 study conducted by the National Institute of Advanced
Studies [21] examined who and why was moving out of the rapidly uplifting neighbourhood of Hayes
Valley in San Francisco. Researchers found that about one fourth of the movers between 1975-1979
left involuntarily, and were mainly black, elder or poor. More recent studies [19, 18] analyse the
prevalence and characteristics of displacement using Milwaukee Area Renters Study survey data.
The elevated costs and limited availability of survey data have encouraged alternative methods
Date: December 12, 2025.
2020 Mathematics Subject Classification. 30L15, 53C23, 53C20, 55N31.
Key words and phrases. Gentrification, Persistent homology, Displacement, Topological Data Analysis, Cubical
complex.
1 Department of Quantitative Methods, CUNEF Universidad, Madrid, Spain. rita.rodriguez@cunef.edu.
2 Department of Mathematics, CUNEF Universidad, Madrid, Spain. manuel.mellado@cunef.edu.
A M. Cuerno has been financially supported by the project “Charting political ideological landscapes in Europe:
Fault lines and opportunities (POL-AXES)” - Programa Primas y Problemas 2023 from Fundaci´on BBVA, and
PID2021-124195NB-C32 and PID2024-158664NB-C22 from the Ministerio de Econom´ıa y Competitividad de Espa˜na
(MINECO).
1
arXiv:2512.10753v1 [cs.CG] 11 Dec 2025
that infer displacement indirectly through socio-economic indicators, either by contrasting these
measures between in-movers and out-movers or interpreting spikes as evidence of displacement.
For instance, [24] investigates exit rates of low-income residents in neighbourhoods with increasing
income, while McKinnish et al. [35] focus on exit rates among vulnerable groups. Other studies
compare a metrics’s value in a neighbourhood with that in a control group: Ding et al.
[20]
contrast mobility rates and destination outcomes between gentrifying and non-gentrifying tracts
in Philadelphia, and Ellen et al.
[23] compare demographic changes in gentrifying tracts with
those in the metropolitan area to assess whether observed shifts indicate displacement or citywide
dynamics. Finally, composite indices such as the Los Angeles Index of Displacement Pressure [38]
weigh individual, household, and neighbourhood indicators to assess relative risk.
These approaches present a series of shortcomings, which fall into two categories. The first and
perhaps the most important one is the lack of replicability to other cities and time periods, which is
due to ad-hoc methodologies and data. Specifically, the choice of a metric and a control group lead
to different definitions thereof, hindering the comparison of displacement r
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