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GeoJournal

, Volume 80, Issue 1, pp 1–13 | Cite as

Geospatial analysis requires a different way of thinking: the problem of spatial heterogeneity

  • Bin Jiang
Article

Abstract

Geospatial analysis is very much dominated by a Gaussian way of thinking, which assumes that things in the world can be characterized by a well-defined mean, i.e., things are more or less similar in size. However, this assumption is not always valid. In fact, many things in the world lack a well-defined mean, and therefore there are far more small things than large ones. This paper attempts to argue that geospatial analysis requires a different way of thinking—a Paretian way of thinking that underlies skewed distribution such as power laws, Pareto and lognormal distributions. I review two properties of spatial dependence and spatial heterogeneity, and point out that the notion of spatial heterogeneity in current spatial statistics is only used to characterize local variance of spatial dependence. I subsequently argue for a broad perspective on spatial heterogeneity, and suggest it be formulated as a scaling law. I further discuss the implications of Paretian thinking and the scaling law for better understanding of geographic forms and processes, in particular while facing massive amounts of social media data. In the spirit of Paretian thinking, geospatial analysis should seek to simulate geographic events and phenomena from the bottom up rather than correlations as guided by Gaussian thinking.

Keywords

Big data Scaling of geographic space Head/tail breaks Power laws Heavy-tailed distributions 

Notes

Acknowledgments

The author would like to thank the anonymous referees and the editor Daniel Z. Sui for their valuable comments. However, any shortcoming remains the responsibility of the author.

References:

  1. Anderson, C. (2006). The long tail: Why the future of business is selling less of more. New York: Hyperion.Google Scholar
  2. Anselin, L. (1989). What is special about spatial data: Alternative perspectives on spatial data analysis. Santa Barbara, CA: National Center for Geographic Information and Analysis.Google Scholar
  3. Anselin, L. (1995). Local indicators of spatial association—LISA. Geographical Analysis, 27, 93–115.CrossRefGoogle Scholar
  4. Bak, P. (1996). How nature works: The science of self-organized criticality. New York: Springer.CrossRefGoogle Scholar
  5. Barabási, A. (2010). Bursts: The hidden pattern behind everything we do. Boston, Massachusetts: Dutton Adult.Google Scholar
  6. Barabási, A.-L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286(5439), 509–512.CrossRefGoogle Scholar
  7. Batty, M., Carvalho, R., Hudson-Smith, A., Milton, R., Smith, D., & Steadman, P. (2008). Scaling and allometry in the building geometries of Greater London. The European Physical Journal B, 63(3), 303–314.CrossRefGoogle Scholar
  8. Batty, M., & Longley, P. (1994). Fractal cities: A geometry of form and function. London: Academic Press.Google Scholar
  9. Benguigui, L., & Czamanski, D. (2004). Simulation analysis of the fractality of cities. Geographical Analysis, 36(1), 69–84.CrossRefGoogle Scholar
  10. Blumenfeld-Lieberthal, E., & Portugali, J. (2010). Network cities: A complexity-network approach to urban dynamics and development. In B. Jiang & X. Yao (Eds.), Geospatial analysis of urban structure and dynamics (pp. 77–90). Berlin: Springer.CrossRefGoogle Scholar
  11. Bonner, J. T. (2006). Why size matters: From bacteria to blue whales. Princeton: Princeton University Press.Google Scholar
  12. Brockmann, D., Hufnage, L., & Geisel, T. (2006). The scaling laws of human travel. Nature, 439, 462–465. http://www.nature.com/nature/journal/v439/n7075/full/nature04292.html.CrossRefGoogle Scholar
  13. Carvalho, R., & Penn, A. (2004). Scaling and universality in the micro-structure of urban space. Physica A, 332, 539–547.CrossRefGoogle Scholar
  14. Chen, Y. (2009). Spatial interaction creates period-doubling bifurcation and chaos of urbanization. Chaos, Solitons & Fractals, 42(3), 1316–1325.CrossRefGoogle Scholar
  15. Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009). Power-law distributions in empirical data. SIAM Review, 51(4), 661–703.CrossRefGoogle Scholar
  16. Cliff, A. D., & Ord, J. K. (1969). The problem of spatial autocorrelation. In A. J. Scott (Ed.), London papers in regional science (pp. 25–55). London: Pion.Google Scholar
  17. Epstein, J. M., & Axtell, R. (1996). Growing artificial societies: Social science from the bottom up. Washington, DC: Brookings Institution Press.Google Scholar
  18. Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically weighted regression: The analysis of spatially varying relationships. Chichester: Wiley.Google Scholar
  19. Getis, A., & Ord, J. K. (1992). The analysis of spatial association by distance statistics. Geographical Analysis, 24(3), 189–206.CrossRefGoogle Scholar
  20. Gonzalez, M., Hidalgo, C. A., & Barabási, A.-L. (2008). Understanding individual human mobility patterns. Nature, 453, 779–782.CrossRefGoogle Scholar
  21. Goodchild, M. (2004). The validity and usefulness of laws in geographic information science and geography. Annals of the Association of American Geographers, 94(2), 300–303.CrossRefGoogle Scholar
  22. Goodchild, M. F. (2007). Citizens as sensors: The world of volunteered geography. GeoJournal, 69(4), 211–221.CrossRefGoogle Scholar
  23. Goodchild, M. F., & Mark, D. M. (1987). The fractal nature of geographic phenomena. Annals of the Association of American Geographers, 77(2), 265–278.CrossRefGoogle Scholar
  24. Griffith, D. A. (2003). Spatial autocorrelation and spatial filtering: Gaining understanding through theory and scientific visualization. Berlin: Springer.CrossRefGoogle Scholar
  25. Guimerà, R., Mossa, S., Turtschi, A., & Amaral, L. A. N. (2005). The worldwide air transportation network: Anomalous centrality, community structure, and cities’ global roles. Proceedings of the National Academy of Sciences of the United States of America, 102(22), 7794–7799.CrossRefGoogle Scholar
  26. Hack J. (1957). Studies of longitudinal stream profiles in Virginia and Maryland. U.S. Geological Survey Professional Paper, 294-B, 41–94.Google Scholar
  27. Horton, R. E. (1945). Erosional development of streams and their drainage basins: Hydrological approach to quantitative morphology. Bulletin of the Geographical Society of America, 56(3), 275–370.CrossRefGoogle Scholar
  28. Jenks, G. F. (1967). The data model concept in statistical mapping. International Yearbook of Cartography, 7, 186–190.Google Scholar
  29. Jiang, B. (2009). Street hierarchies: A minority of streets account for a majority of traffic flow. International Journal of Geographical Information Science, 23(8), 1033–1048.CrossRefGoogle Scholar
  30. Jiang, B. (2013a). Head/tail breaks: A new classification scheme for data with a heavy-tailed distribution. The Professional Geographer, 65(3), 482–494.CrossRefGoogle Scholar
  31. Jiang, B. (2013b). The image of the city out of the underlying scaling of city artifacts or locations. Annals of the Association of American Geographers, 103(6), 1552–1566.CrossRefGoogle Scholar
  32. Jiang, B., & Jia, T. (2011). Zipf’s law for all the natural cities in the United States: A geospatial perspective. International Journal of Geographical Information Science, 25(8), 1269–1281.CrossRefGoogle Scholar
  33. Jiang, B., & Liu, X. (2012). Scaling of geographic space from the perspective of city and field blocks and using volunteered geographic information. International Journal of Geographical Information Science, 26(2), 215–229.CrossRefGoogle Scholar
  34. Jiang, B., & Miao, Y. (2014). The evolution of natural cities from the perspective of location-based social media. The University of Gävle working paper. Gävle, Sweden.Google Scholar
  35. Jiang, B., & Yin, J. (2013). Ht-index for quantifying the fractal or scaling structure of geographic features. Annals of the Association of American Geographers,. doi: 10.1080/00045608.2013.834239.Google Scholar
  36. Jiang, B., Yin, J., & Zhao, S. (2009). Characterizing human mobility patterns in a large street network. Physical Review E, 80(2), 021136.CrossRefGoogle Scholar
  37. Koch, R. (1999). The 80/20 Principle: The secret to achieving more with less. New York: Crown Business.Google Scholar
  38. Krugman, P. (1996). The Self-Organizing Economy. Cambridge, Massachusetts: Blackwell.Google Scholar
  39. Kyriakidou, V., Michalakelis, C., & Varoutas, D. (2011). Applying Zipf’s power law over population density and growth as network deployment indicator. Journal of Service Science and Management, 4(2), 132–140.CrossRefGoogle Scholar
  40. Lämmer, S., Gehlsen, B., & Helbing, D. (2006). Scaling laws in the spatial structure of urban road networks. Physica A, 363(1), 89–95.CrossRefGoogle Scholar
  41. Lin, Y. (2013). A comparison study on natural and head/tail breaks involving digital elevation models. Bachelor Thesis at University of Gävle, Sweden.Google Scholar
  42. Mandelbrot, B. (1967). How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science, 156(3775), 636–638.Google Scholar
  43. Mandelbrot, B. B. (1982). The fractal geometry of nature. San Francisco: W. H. Freeman.Google Scholar
  44. Mandelbrot, B. B., & Hudson, R. L. (2004). The (mis)behavior of markets: A fractal view of risk, ruin and reward. New York: Basic Books.Google Scholar
  45. Maritan, A., Rinaldo, A., Rigon, R., Giacometti, A., & Rodríguez-Iturbe, I. (1996). Scaling laws for river networks. Physical Review E, 53(2), 1510–1515.CrossRefGoogle Scholar
  46. Mayer-Schonberger, V., & Cukier, K. (2013). Big data: A revolution that will transform how we live, work, and think. New York: Eamon Dolan/Houghton Mifflin Harcourt.Google Scholar
  47. McKelvey, B., & Andriani, P. (2005). Why Gaussian statistics are mostly wrong for strategic organization. Strategic Organization, 3(2), 219–228.CrossRefGoogle Scholar
  48. Montello, D. R. (2001). Scale in geography. In N. J. Smelser & P. B. Baltes (Eds.), International encyclopedia of the social & behavioral sciences (pp. 13501–13504). Oxford: Pergamon Press.CrossRefGoogle Scholar
  49. Newman, M. (2011). Complex systems: A survey. http://arxiv.org/abs/1112.1440.
  50. Pareto, V. (1897). Cours d’économie politique. Lausanne: Ed. Rouge.Google Scholar
  51. Pelletier, J. D. (1999). Self-organization and scaling relationships of evolving river networks. Journal of Geophysical Research, 104(B4), 7359–7375.CrossRefGoogle Scholar
  52. Pumain, D. (2006). Hierarchy in natural and social sciences. Dordrecht: Springer.CrossRefGoogle Scholar
  53. Salingaros, N. A., & West, B. J. (1999). A universal rule for the distribution of sizes. Environment and Planning B: Planning and Design, 26(6), 909–923.CrossRefGoogle Scholar
  54. Schaefer, J. A., & Mahoney, A. P. (2003). Spatial and temporal scaling of population density and animal movement: A power law approach. Ecoscience, 10(4), 496–501.Google Scholar
  55. Schroeder, M. (1991). Chaos, fractals, power laws: Minutes from an infinite paradise. New York: Freeman.Google Scholar
  56. Taleb, N. N. (2007). The Black Swan: The impact of the highly improbable. London: Allen Lane.Google Scholar
  57. Tobler, W. (1970). A computer movie simulating urban growth in the Detroit region. Economic Geography, 46(2), 234–240.CrossRefGoogle Scholar
  58. Wu, J., & Li, H. (2006). Concepts of scale and scaling. In J. Wu, K. B. Jones, H. Li, & O. L. Loucks (Eds.), Scaling and uncertainty analysis in ecology (pp. 3–15). Berlin: Springer.CrossRefGoogle Scholar
  59. Zipf, G. K. (1949). Human behavior and the principles of least effort. Cambridge, MA: Addison Wesley.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Division of Geomatics, Department of Technology and Built EnvironmentUniversity of GävleGävleSweden

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