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Multidimensional urban segregation: toward a neural network measure

  • WSOM 2017
  • Published:
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Abstract

We introduce a multidimensional, neural network approach to reveal and measure urban segregation phenomena, based on the self-organizing map algorithm (SOM). The multidimensionality of SOM allows one to apprehend a large number of variables simultaneously, defined on census blocks or other types of statistical blocks, and to perform clustering along them. Levels of segregation are then measured through correlations between distances on the neural network and distances on the actual geographical map. Further, the stochasticity of SOM enables one to quantify levels of heterogeneity across census blocks. We illustrate this new method on data available for the city of Paris.

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Notes

  1. These are social benefits paid to prevent people from falling into extreme poverty. They vary from 300 euros to about 800 euros per month.

  2. Note that such a simple, direct measure of the correlation between geographical distance and Kohonen distance is well suited to intricate patterns of segregation, as observed in real cities. However, if one considers artificial patterns with much regularity, this correlation measure works well on checker-board patterns (provided the mesh is not too small), but obviously not as well on concentric patterns. More work is needed to circumvent this difficulty.

References

  1. Intégration des stations du réseau ferré RATP (2012). http://openstreetmap.fr/blogs/cquest/stations-ratp. Accessed March 2017

  2. Arribas-Bel D, Nijkamp P, Scholten H (2011) Multidimensional urban sprawl in Europe: a self-organizing map approach. Comput Environ Urban Syst 35(4):263–275

    Google Scholar 

  3. Banos A (2012) Network effects in Schelling’s model of segregation: new evidence from agent-based simulation. Environ Plan B Plan Des 39(2):393–405

    Google Scholar 

  4. Batty M (1976) Entropy in spatial aggregation. Geogr Anal 8(1):1–21

    MathSciNet  Google Scholar 

  5. Benenson I, Hatna E, Or E (2009) From Schelling to spatially explicit modeling of urban ethnic and economic residential dynamics. Sociol Methods Res 37(4):463–497

    MathSciNet  Google Scholar 

  6. de Bodt E, Cottrell M, Verleysen M (2002) Statistical tools to assess the reliability of self-organizing maps. Neural Netw 15(8–9):967–978

    MATH  Google Scholar 

  7. Boelaert J, Bendhaiba L, Olteanu M, Villa-Vialaneix N (2014) SOMbrero: an R package for numeric and non-numeric self-organizing maps. Springer, Berlin, pp 219–228

    Google Scholar 

  8. Bourgeois N, Cottrell M, Déruelle B, Lamassé S, Letrémy P (2015) How to improve robustness in Kohonen maps and display additional information in factorial analysis: application to text mining. Neurocomputing 147:120–135

    Google Scholar 

  9. Bourgeois N, Cottrell M, Lamassé S, Olteanu M (2015) Search for meaning through the study of co-occurrences in texts. International work-conference on artificial neural networks. Springer, Berlin, pp 578–591

    Google Scholar 

  10. Castellano C, Fortunato S, Loreto V (2009) Statistical physics of social dynamics. Rev Mod Phys 81(2):591

    Google Scholar 

  11. Clark WA (1991) Residential preferences and neighborhood racial segregation: a test of the Schelling segregation model. Demography 28(1):1–19

    Google Scholar 

  12. Clark WA, Fossett M (2008) Understanding the social context of the Schelling segregation model. Proc Natl Acad Sci 105(11):4109–4114

    Google Scholar 

  13. Cortez V, Medina P, Goles E, Zarama R, Rica S et al (2015) Attractors, statistics and fluctuations of the dynamics of the Schelling’s model for social segregation. Eur Phys J B 88:25

    Google Scholar 

  14. Cottrell M, Olteanu M, Randon-Furling J, Hazan A (2017) Multidimensional urban segregation: an exploratory case study. In: 2017 12th International workshop on self-organizing maps and learning vector quantization, clustering and data visualization (WSOM). IEEE, pp 1–7

  15. Crane J (1991) The epidemic theory of ghettos and neighborhood effects on dropping out and teenage childbearing. Am. J Sociol 96(5):1226–1259

    Google Scholar 

  16. Dall’Asta L, Castellano C, Marsili M (2008) Statistical physics of the Schelling model of segregation. J Stat Mech Theory Exp 07:L07002

    Google Scholar 

  17. Durrett R, Zhang Y (2014) Exact solution for a metapopulation version of Schelling’s model. Proc Natl Acad Sci 111(39):14036–14041

    MathSciNet  MATH  Google Scholar 

  18. Feitosa FF, Camara G, Monteiro AMV, Koschitzki T, Silva MP (2007) Global and local spatial indices of urban segregation. Int J Geogr Inf Sci 21(3):299–323

    Google Scholar 

  19. Gauvin L, Nadal JP, Vannimenus J (2010) Schelling segregation in an open city: a kinetically constrained Blume–Emery–Griffiths spin-1 system. Phys Rev E 81(6):066120

    Google Scholar 

  20. Gauvin L, Vannimenus J, Nadal JP (2009) Phase diagram of a Schelling segregation model. Eur Phys J B 70(2):293–304

    Google Scholar 

  21. Grauwin S, Bertin E, Lemoy R, Jensen P (2009) Competition between collective and individual dynamics. Proc Natl Acad Sci 106(49):20622–20626

    Google Scholar 

  22. Hatna E, Benenson I (2012) The Schelling model of ethnic residential dynamics: beyond the integrated-segregated dichotomy of patterns. J Artif Soc Soc Simul 15(1):6

    Google Scholar 

  23. Hatna E, Benenson I (2015) Combining segregation and integration: Schelling model dynamics for heterogeneous population. J Artif Soc Soc Simul 18(4):1–15

    Google Scholar 

  24. Hazan A, Randon-Furling J (2013) A Schelling model with switching agents: decreasing segregation via random allocation and social mobility. Eur Phys J B 86(10):1–9

    MathSciNet  Google Scholar 

  25. Henry AD, Prałat P, Zhang CQ (2011) Emergence of segregation in evolving social networks. Proc Natl Acad Sci 108(21):8605–8610

    MathSciNet  MATH  Google Scholar 

  26. Hong SY, O’Sullivan D, Sadahiro Y (2014) Implementing spatial segregation measures in R. PloS ONE 9(11):e113767

    Google Scholar 

  27. Iceland J (2004) The multigroup entropy index. US Census Bur 31:2006

    Google Scholar 

  28. Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43(1):59–69

    MathSciNet  MATH  Google Scholar 

  29. Kohonen T (2012) Self-organizing maps. Springer series in information sciences. Springer, Berlin

    MATH  Google Scholar 

  30. Laurie AJ, Jaggi NK (2003) Role of “vision” in neighbourhood racial segregation: a variant of the Schelling segregation model. Urban Stud 40(13):2687–2704

    Google Scholar 

  31. Macy MW, Willer R (2002) From factors to factors: computational sociology and agent-based modeling. Ann Rev Sociol 28(1):143–166

    Google Scholar 

  32. Pancs R, Vriend NJ (2007) Schelling’s spatial proximity model of segregation revisited. J Public Econ 91(1):1–24

    Google Scholar 

  33. Pollicott M, Weiss H (2001) The dynamics of Schelling-type segregation models and a nonlinear graph laplacian variational problem. Adv Appl Math 27(1):17–40

    MathSciNet  MATH  Google Scholar 

  34. Reardon SF, Firebaugh G (2002) Measures of multigroup segregation. Sociol Methodol 32(1):33–67

    Google Scholar 

  35. Reardon SF, O’Sullivan D (2004) Measures of spatial segregation. Sociol Methodol 34(1):121–162

    Google Scholar 

  36. Rogers T (2011) A unified framework for Schelling’s model of segregation. J Stat Mech Theory Exp 07:P07006

    MATH  Google Scholar 

  37. Sahasranaman A, Jensen HJ (2016) Dynamics of transformation from segregation to mixed wealth cities. PloS ONE 11(11):e0166960

    Google Scholar 

  38. Schelling TC (1969) Models of segregation. Am Econ Rev 59(2):488–493

    Google Scholar 

  39. Schelling TC (1971) Dynamic models of segregation. J Math Sociol 1(2):143–186

    MATH  Google Scholar 

  40. Singh A, Vainchtein D, Weiss H (2009) Schelling’s segregation model: parameters, scaling, and aggregation. Demogr Res 21:341

    Google Scholar 

  41. Stauffer D, Solomon S (2007) Ising, Schelling and self-organising segregation. Eur Phys J B 57(4):473–479

    Google Scholar 

  42. Theil H, Finizza AJ (1971) A note on the measurement of racial integration of schools by means of informational concepts. Taylor & Francis, Routledge

    Google Scholar 

  43. Vinković D, Kirman A (2006) A physical analogue of the Schelling model. Proc Natl Acad Sci 103(51):19261–19265

    Google Scholar 

  44. Wei C, Cabrera-Barona P, Blaschke T (2016) Local geographic variation of public services inequality: does the neighborhood scale matter? Int J Environ Res Public Health 13(10):981

    Google Scholar 

  45. Wu Q, Cheng J, Chen G, Hammel DJ, Wu X (2014) Socio-spatial differentiation and residential segregation in the Chinese city based on the 2000 community-level census data: a case study of the inner city of Nanjing. Cities 39:109–119

    Google Scholar 

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Authors and Affiliations

  1. SAMM (EA4543), Université Paris 1 Panthéon-Sorbonne, Paris, France

    Madalina Olteanu, Marie Cottrell & Julien Randon-Furling

  2. LISSI (EA 3956), Senart-FB Institute of Technology, Université Paris-Est, Lieusaint, France

    Aurélien Hazan

  3. MaIAGE, INRA, Université Paris-Saclay, Jouy-en-Josas, France

    Madalina Olteanu

Authors
  1. Madalina Olteanu
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  2. Aurélien Hazan
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  3. Marie Cottrell
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  4. Julien Randon-Furling
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Correspondence to Julien Randon-Furling.

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Olteanu, M., Hazan, A., Cottrell, M. et al. Multidimensional urban segregation: toward a neural network measure. Neural Comput & Applic 32, 18179–18191 (2020). https://doi.org/10.1007/s00521-019-04199-5

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