The Endpoint Hypothesis: A Topological-Cognitive Assessment of Geographic Scale Movement Patterns

  • Alexander Klippel
  • Rui Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5756)


Movement patterns of individual entities at the geographic scale are becoming a prominent research focus in spatial sciences. One pertinent question is how cognitive and formal characterizations of movement patterns relate. In other words, are (mostly qualitative) formal characterizations cognitively adequate? This article experimentally evaluates movement patterns that can be characterized as paths through a conceptual neighborhood graph, that is, two extended spatial entities changing their topological relationship gradually. The central questions addressed are: (a) Do humans naturally use topology to create cognitive equivalent classes, that is, is topology the basis for categorizing movement patterns spatially? (b) Are ‘all’ topological relations equally salient, and (c) does language influence categorization. The first two questions are addressed using a modification of the endpoint hypothesis stating that: movement patterns are distinguished by the topological relation they end in. The third question addresses whether language has an influence on the classification of movement patterns, that is, whether there is a difference between linguistic and non-linguistic category construction. In contrast to our previous findings we were able to document the importance of topology for conceptualizing movement patterns but also reveal differences in the cognitive saliency of topological relations. The latter aspect calls for a weighted conceptual neighborhood graph to cognitively adequately model human conceptualization processes.


Movement Pattern Spatial Relation Spatial Cognition Topological Relation Linguistic Label 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Ahlqvist, O.: A parametrized representation of uncertain conceptual spaces. Transactions in GIS 8(4), 493–514 (2004)CrossRefGoogle Scholar
  2. Ahn, W.-K., Goldstone, R.L., Love, B.C., Markman, A.B., Wolff, P. (eds.): Decade of behavior 2000-2010. Categorization inside and outside the laboratory: Essays in honor of Douglas L. Medin. American Psychological Assoc., Washington (2005)Google Scholar
  3. Allen, J.F.: Maintaining knowledge about temporal intervals. Communications of the ACM 26, 832–843 (1983)CrossRefMATHGoogle Scholar
  4. Barsalou, L.W.: Perceptual symbol systems. Behavioral and Brain Sciences 22(4), 577–609 (1999)Google Scholar
  5. Barsalou, L.W.: Abstraction in perceptual symbol systems. Philosophical Transactions of the Royal Society of London: Biological Sciences 358, 1177–1187 (2003)CrossRefGoogle Scholar
  6. Biederman, I.: Recognition-by-components: A theory of human image understanding. Psychological Review 94, 115–145 (1987)CrossRefGoogle Scholar
  7. Boroditsky, L.: Does language shape thought?: Mandarin and English speakers’ conceptions of time. Cognitive Psychology 43, 1–22 (2001)CrossRefGoogle Scholar
  8. Bryant, R.: Discovery and decision: Exploring the metaphysics and epistemology of scientific classification. Fairleigh Dickinson University Press Associated Univ. Presses, Madison N.J (2000)Google Scholar
  9. Camara, K., Jungert, E.: A visual query language for dynamic processes applied to a scenario driven environment. Journal of Visual Languages and Computing 18, 315–338 (2007)CrossRefGoogle Scholar
  10. Cohn, A.G.: Qualitative Spatial Representation and Reasoning Techniques. In: Brewka, G., Habel, C., Nebel, B. (eds.) Advances in Articial Intelligence KI 1997, pp. 1–30. Springer, Berlin (1997)Google Scholar
  11. Crawford, L.E., Regier, T., Huttenlocher, J.: Linguistic and non- linguistic spatial categorization. Cognition 75(3), 209–235 (2000)CrossRefGoogle Scholar
  12. Dodge, S., Weibel, R., Lautenschütz, A.K.: Towards a taxonomy of movement patterns. Information Visualization 7, 240–252 (2008)CrossRefGoogle Scholar
  13. Egenhofer, M.J., Al-Taha, K.K.: Reasoning about gradual changes of topological relationships. In: Frank, A.U., Formentini, U., Campari, I. (eds.) GIS 1992. LNCS, vol. 639, pp. 196–219. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  14. Egenhofer, M.J., Franzosa, R.D.: Point-set topological spatial relations. International Journal of Geographical Information Systems 5(2), 161–174 (1991)CrossRefGoogle Scholar
  15. Freksa, C.: Temporal reasoning based on semi-intervals. Artificial Intelligence 54(1), 199–227 (1992)MathSciNetCrossRefGoogle Scholar
  16. Freksa, C., Habel, C., Wender, K.F. (eds.): Spatial Cognition 1998. LNCS, vol. 1404. Springer, Heidelberg (1998)Google Scholar
  17. Furnas, G.W., Landauer, T.K., Gomez, L.M., Dumais, S.T.: The vocabulary problem in human-system communication. Commun. ACM 30(11), 964–971 (1987)CrossRefGoogle Scholar
  18. Galton, A.: Fields and objects in space, time, and space-time. Spatial Cognition and Computation 4(1), 39–68 (2004)CrossRefGoogle Scholar
  19. Gibson, J.: The ecological approach to visual perception. Houghton Mifflin, Boston (1979)Google Scholar
  20. Goldstone, R.: The role of similarity in categorization: Providing a groundwork. Cognition 52(2), 125–157 (1994)CrossRefGoogle Scholar
  21. Goldstone, R.L., Barsalou, L.W.: Reuniting perception and conception. Cognition 65, 231–262 (1998)CrossRefGoogle Scholar
  22. Hayes, P.: The naive physics manifesto. In: Michie, D. (ed.) Expert Systems in the Microelectronic Age, pp. 242–270. Edinburgh University Press, Edinburgh (1978)Google Scholar
  23. Hobbs, J.R.: Granularity. In: Joshi, A.K. (ed.) Proceedings of the 9th International Joint Conference on Artificial Intelligence, Los Angeles, CA, pp. 432–435. Morgan Kaufmann, San Francisco (1985)Google Scholar
  24. Hornsby, K., Egenhofer, M.J.: Qualitative representation of change. In: Frank, A.U. (ed.) COSIT 1997. LNCS, vol. 1329, pp. 15–33. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  25. January, D., Kako, E.: Re-evaluating evidence for linguistic relativity: Reply to Boroditsky (2001). Cognition 104, 417–426 (2007)CrossRefGoogle Scholar
  26. Klippel, A., Hardisty, F., Weaver, C.: Star plots: How shape characteristics influence classification tasks. Cartography and Geographic Information Science 36(2), 149–163 (2009)CrossRefGoogle Scholar
  27. Klippel, A., Montello, D.R.: Linguistic and nonlinguistic turn direction concepts. In: Winter, S., Duckham, M., Kulik, L., Kuipers, B. (eds.) COSIT 2007. LNCS, vol. 4736, pp. 354–372. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  28. Klippel, A., Worboys, M., Duckham, M.: Identifying factors of geographic event conceptualisation. International Journal of Geographical Information Science 22(2), 183–204 (2008)CrossRefGoogle Scholar
  29. Klippel, A.: Topologically characterized movement patterns – A cognitive assessment. In: Spatial Cognition and Computation (to appear)Google Scholar
  30. Knauff, M., Rauh, R., Renz, J.: A cognitive assessment of topological spatial relations: Results from an empirical investigation. In: Frank, A.U. (ed.) COSIT 1997. LNCS, vol. 1329, pp. 193–206. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  31. Kos, A.J., Psenicka, C.: Measuring cluster similarity across methods. Psychological Reports 86, 858–862 (2000)CrossRefGoogle Scholar
  32. Kuhn, W.: An image-schematic account of spatial categories. In: Winter, S., Duckham, M., Kulik, L., Kuipers, B. (eds.) COSIT 2007. LNCS, vol. 4736, pp. 152–168. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  33. Lakoff, G.: Women, fire and dangerous things. Chicago University Press, Chicago (1987)CrossRefGoogle Scholar
  34. Laurence, S., Margolis, E.: Concepts and cognitive science. In: Margolis, E., Laurence, S. (eds.) Concepts. Core readings, pp. 3–81. MIT Press, Cambridge (1999)Google Scholar
  35. Lu, S., Harter, D.: The role of overlap and end state in perceiving and remembering events. In: Sun, R. (ed.) The 28th Annual Conference of the Cognitive Science Society, Vancouver, British Columbia, Canada, pp. 1729–1734. Lawrence Erlbaum, Mahwah (2006)Google Scholar
  36. Mark, D.M., Comas, D., Egenhofer, M.J., Freundschuh, S.M., Gould, M.D., Nunes, J.: Evaluation and refining computational models of spatial relations through cross-linguistic human-subjects testing. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 553–568. Springer, Heidelberg (1995)Google Scholar
  37. Mark, D.M., Egenhofer, M.J.: Modeling spatial relations between lines and regions: Combining formal mathematical models and human subject testing. Cartography and Geographic Information Systems 21(3), 195–212 (1994)Google Scholar
  38. McIntosh, J., Yuan, M.: Assessing similarity of geographic processes and events. Transactions in GIS 9(2), 223–245 (2005)CrossRefGoogle Scholar
  39. Medin, D.L., Wattenmaker, W.D., Hampson, S.E.: Family resemblance, conceptual cohesiveness, and category construction. Cognitive Psychology 19(2), 242–279 (1987)CrossRefGoogle Scholar
  40. Mennis, J., Peuquet, D.J., Qian, L.: A conceptual framework for incorporating cognitive principles into geographical database representation. International Journal of Geographical Information Science 14(6), 501–520 (2000)CrossRefGoogle Scholar
  41. Montello, D.R., Frank, A.U.: Modeling directional knowledge and reasoning in environmental space: Testing qualitative metrics. In: Portugali, J. (ed.) The construction of cognitive maps, pp. 321–344. Kluwer, Dodrecht (1996)CrossRefGoogle Scholar
  42. Murphy, G.L., Medin, D.L.: The role of theories in conceptual coherence. Psychological Review 92(3), 289–316 (1985)CrossRefGoogle Scholar
  43. Nedas, K.A., Egenhofer, M.J.: Integral vs. Separable attributes in spatial similarity assessments. In: Freksa, C., Newcombe, N.S., Gärdenfors, P., Wölfl, S. (eds.) Spatial Cognition VI. LNCS, vol. 5248, pp. 295–310. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  44. Peuquet, D.J.: Making space for time: Issues in space-time data representation. GeoInformatica 5(1), 11–32 (2001)CrossRefMATHGoogle Scholar
  45. Piaget, J.: The construction of reality in the child. Basic Books, New York (1955)Google Scholar
  46. Pothos, E.M., Chater, N.: A simplicity principle in unsupervised human categorization. Cognitive Science 26(3), 303–343 (2002)CrossRefGoogle Scholar
  47. Pothos, E.M., Close, J.: One or two dimensions in spontaneous classification: A simplicity approach. Cognition (2), 581–602 (2008)CrossRefGoogle Scholar
  48. Ragni, M., Tseden, B., Knauff, M.: Cross-cultural similarities in topological reasoning. In: Winter, S., Duckham, M., Kulik, L., Kuipers, B. (eds.) COSIT 2007. LNCS, vol. 4736, pp. 32–46. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  49. Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connections. In: Proceedings 3rd International Conference on Knowledge Representation and Reasoning, pp. 165–176. Morgan Kaufmann, San Francisco (1992)Google Scholar
  50. Regier, T., Zheng, M.: Attention to endpoints: A cross-linguistic constraint on spatial meaning. Cognitive Science 31(4), 705–719 (2007)CrossRefGoogle Scholar
  51. Renz, J. (ed.): Qualitative Spatial Reasoning with Topological Information. LNCS (LNAI), vol. 2293. Springer, Heidelberg (2002)MATHGoogle Scholar
  52. Riedemann, C.: Matching names and definitions of topological operators. In: Cohn, A.G., Mark, D.M. (eds.) COSIT 2005. LNCS, vol. 3693, pp. 165–181. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  53. Rips, L.J.: Similarity, typicality and categorisation. In: Vosniadou, S., Ortony, A. (eds.) Similarity and Analogical Reasoning, pp. 21–59. Cambridge University Press, Cambridge (1989)CrossRefGoogle Scholar
  54. Rosch, E.: Cognitive representations of semantic categories. Journal of Experimental Psychology: General 104(3), 192–233 (1975)CrossRefGoogle Scholar
  55. Schwering, A.: Evaluation of a semantic similarity measure for natural language spatial relations. In: Winter, S., Duckham, M., Kulik, L., Kuipers, B. (eds.) COSIT 2007. LNCS, vol. 4736, pp. 116–132. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  56. Schwering, A.: Approaches to semantic similarity measurement for geo-spatial data: A survey. Transactions in GIS 12(1), 2–29 (2008)CrossRefGoogle Scholar
  57. Schwering, A., Kuhn, W.: A hybrid semantic similarity measure for spatial information retrieval. In: Spatial Cognition and Computation (to appear)Google Scholar
  58. Shipley, T.F., Zacks, J.M. (eds.): Understanding events: How humans see, represent, and act on events. Oxford University Press, New York (2008)Google Scholar
  59. Strube, G.: The Role of Cognitive Science in Knowledge Engineering. In: Schmalhofer, F., Strube, G., Wetter, T. (eds.) GI-Fachtagung 1991. LNCS, vol. 622, pp. 161–174. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  60. Weaver, C.: Building highly-coordinated visualizations in improvise. In: Proceedings of the IEEE Symposium on Information Visualization 2004, Austin, TX (October 2004)Google Scholar
  61. Wishart, D.: ClustanGraphics Primer: A guide to cluster analysis, 3rd edn. Clustan Limited, Edinburgh (2004)Google Scholar
  62. Worboys, M., Duckham, M.: Monitoring qualitative spatiotemporal change for geosensor networks. International Journal of Geographical Information Science 20(10), 1087–1108 (2006)CrossRefGoogle Scholar
  63. Xu, J.: Formalizing natural-language spatial relations between linear objects with topological and metric properties. International Journal of Geographical Information Science 21(4), 377–395 (2007)MathSciNetCrossRefGoogle Scholar
  64. Yuille, A.L., Ullman, S.: Computational theories of low-level vision. In: Osherson, D.N., Kosslyn, S.M., Hollerback, J.M. (eds.) An invitation to cognitive science: Language, vol. 2, pp. 5–39. MIT Press, Cambridge (1990)Google Scholar
  65. Zacks, J.M., Tversky, B.: Event structure in perception and conception. Psychological Bulletin 127(1), 3–21 (2001)CrossRefGoogle Scholar
  66. Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)MathSciNetCrossRefMATHGoogle Scholar
  67. Zhan, F.B.: A fuzzy set model of approximate linguistic terms in descriptions of binary topological relations between simple regions. In: Matsakis, P., Sztandera, L.M. (eds.) Applying soft computing in defining spatial relations, pp. 179–202. Physica-Verlag, Heidelberg (2002)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Alexander Klippel
    • 1
  • Rui Li
    • 1
  1. 1.Department of Geography, GeoVISTA CenterThe Pennsylvania State UniversityUniversity ParkUSA

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