Spatial Support and Spatial Confidence for Spatial Association Rules

  • Patrick Laube
  • Mark de Berg
  • Marc van Kreveld
Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)


In data mining, the quality of an association rule can be stated by its support and its confidence. This paper investigates support and confidence measures for spatial and spatio-temporal data mining. Using fixed thresholds to determine how many times a rule that uses proximity is satisfied seems too limited. It allows the traditional definitions of support and confidence, but does not allow to make the support stronger if the situation is “really close”, as compared to “fairly close”. We investigate how to define and compute proximity measures for several types of geographic objects—point, linear, areal—and we express whether or not objects are “close” as a score in the range [0, 1]. We then use the theory from so-called fuzzy association rules to determine the support and confidence of an association rule. The extension to spatiotemporal rules can be done along the same lines.


Spatial data mining spatial association rule mining fuzzy association rules support confidence 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. Agrawal, T. Imieliski, and A Swami. Mining association rules between sets of items in large databases. In SIGMOD93. ACM, 1993.Google Scholar
  2. [2]
    M. de Berg, O. Cheong, M. van Kreveld, and M. Overmars. Computational Geometry: Algorithms and Applications. Springer-Verlag, Berlin, 3nd edition, 2008.Google Scholar
  3. [3]
    Didier Dubois, Eyke Hüllermeier, and Henri Prade. A systematic approach to the assessment of fuzzy association rules. Data Min. Knowl. Discov., 13(2):167–192, 2006.Google Scholar
  4. [4]
    M. Erwig. The graph Voronoi diagram with applications. Networks, 36(3):156–163, 2000.CrossRefGoogle Scholar
  5. [5]
    U. Fayyad, G. Piatetsky-Shapiro, and P. Smyth. From data mining to knowledge discovery in databases. AI Magazine, 17(3):37–54, 1996.Google Scholar
  6. [6]
    G. Gidofalvi and T. B. Pedersen. Spatio-temporal rule mining: Issues and techniques. In Data Warehousing and Knowledge Discovery, Proceedings, volume 3589 of Lecture Notes in Computer Science, pages 275–284. Springer-Verlag, Berlin, 2005.Google Scholar
  7. [7]
    J. Gudmundsson, M. van Kreveld, and B. Speckmann. Efficient detection of patterns in 2D trajectories of moving points. GeoInformatica, 11(2):195–215, 2007.CrossRefGoogle Scholar
  8. [8]
    P. Héjek. Metamathematics of Fuzzy Logic.Kluwer, 1998.Google Scholar
  9. [9]
    K. Koperski and J. Han. Discovery of Spatial Association Rules in Geographic Information Databases. Proceedings of the 4th International Symposium on Advances in Spatial Databases. Springer-Verlag, 1995.Google Scholar
  10. [10]
    C.M. Kuok, A.W.-C. Fu, and M.H Wong. Mining fuzzy association rules in databases. SIGMOD Record, 27:41–46, 1998.CrossRefGoogle Scholar
  11. [11]
    P. Laube, S. Imfeld, and R. Weibel.Discovering relative motion patterns in groups of moving point objects. International Journal of Geographical Information Science, 19(6):639–668, 2005.Google Scholar
  12. [12]
    C.-T. Lu, D. Chen, and Y. Kou. Detecting spatial outliers with multiple attributes.In Proceedings of the 15th IEEE International Conference on Tools with Artificial Intelligence 2003 (ICTAI’04), pages 122–128, 2003.Google Scholar
  13. [13]
    H. J. Miller and J. Han. Geographic data mining and knowledge discovery: An overview. In H. J. Miller and J. Han, editors, Geographic data mining and knowledge discovery, pages 3–32. Taylor and Francis, London, UK, 2001.Google Scholar
  14. [14]
    H. J. Miller and E. A. Wentz. Representation and spatial analysis in geographic information systems. Annals of the Association of American Geographers, 93(3):574–594, 2003.CrossRefGoogle Scholar
  15. [15]
    R. T. Ng. Detecting outliers from large datasets. In H. J. Miller and J. Han, editors, Geographic data mining and knowledge discovery, pages 218–235. Taylor and Francis, London, UK, 2001.Google Scholar
  16. [16]
    D. O’Sullivan and D. J. Unwin. Geographic Information Analysis. John Wiley and Sons, Hoboken, NJ, 2003.Google Scholar
  17. [17]
    J. F. Roddick, K. Hornsby, and M. Spiliopoulou. An updated bibliography of temporal, spatial, and spatio-temporal data mining research.In J. F. Roddick and K. Hornsby, editors, Temporal, spatial and spatio-temporal data mining, TSDM 2000, volume 2007 of Lecture Notes in Artificial Intelligence, pages 147–163. Springer, Berlin Heidelberg, DE, 2001.Google Scholar
  18. [18]
    J. F. Roddick and B. G Lees. Paradigms for spatial and spatio-temporal data mining. In H. J. Miller and J. Han, editors, Geographic data mining and knowledge discovery, pages 33–49. Taylor and Francis, London, UK, 2001.Google Scholar
  19. [19]
    Y. Sadahiro. Cluster detection in uncertain point distributions: a comparison of four methods. Computers, Environment and Urban Systems, 27(1):33–52, 2003.CrossRefGoogle Scholar
  20. [20]
    S. Shekhar and Y. Huang. Discovering spatial co-location patterns: A summary of results. In Advances in Spatial and Temporal Databases, Proceedings, volume 2121 of Lecture Notes in Computer Science, pages 236–256. Springer-Verlag, Berlin, 2001.Google Scholar
  21. [21]
    S. Shekhar, C. T. Lu, and P. S. Zhang. A unified approach to detecting spatial outliers. Geoinformatica, 7(2):139–166, 2003.CrossRefGoogle Scholar
  22. [22]
    S. Shekhar, P. Zhang, Y. Huang, and R. R. Vatsavai. Trends in spatial data mining. In H. Kargupta, A. Joshi, K. Sivakumar, and Y. Yesha, editors, Data Mining: Next Generation Challenges and Future Directions. MIT/AAAI Press, 2003.Google Scholar
  23. [23]
    W. R. Tobler. A computer movie simulating urban growth in the Detroit region. Economic Geography, 46(2):234–240, 1970.CrossRefGoogle Scholar
  24. [24]
    F. Verhein and S. Chawla. Mining spatio-temporal association rules, sources, sinks, stationary regions and thoroughfares in object mobility databases. In Database Systems for Advanced Applications, pages 187–201. 2006.Google Scholar
  25. [25]
    F. Verhein and S. Chawla. Mining spatio-temporal patterns in object mobility databases. Data Mining and Knowledge Discovery, 16(1):5–38, 2008.CrossRefGoogle Scholar
  26. [26]
    M. F. Worboys. Metrics and topologies for geographic space. In M. J. Kraak and M. Molenaar, editors, Advances in Geographic Information Systems Research II: Proceedings of the International Symposium on Spatial Data Handling, Delft, pages 365–376, London, UK, 1996. Taylor & Francis.Google Scholar
  27. [27]
    M. F. Worboys. Nearness relations in environmental space. International Journal of Geographical Information Science, 15(7):633–651, 2001.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Patrick Laube
    • 1
  • Mark de Berg
    • 2
  • Marc van Kreveld
    • 3
  1. 1.Geomatics DepartmentThe University of Melbourne3010 Parkville VICAustralia
  2. 2.Department of Mathematics and Computing ScienceTU Eindhoven5600 MB EindhovenThe Netherlands
  3. 3.Department of Computer ScienceUtrecht University3508 TBUtrecht

Personalised recommendations