Region-Restricted Clustering for Geographic Data Mining

  • Joachim Gudmundsson
  • Marc van Kreveld
  • Giri Narasimhan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)


Cluster detection for a set P of n points in geographic situations is usually dependent on land cover or another thematic map layer. This occurs for instance if the points of P can only occur in one land cover type. We extend the definition of clusters to region-restricted clusters, and give efficient algorithms for exact computation and approximation. The algorithm determines all axis-parallel squares with exactly m out of n points inside, size at most some prespepcified value, and area of a given land cover type at most another prespecified value. The exact algorithm runs in O(nmlog2 n + (nm+nn f )log2 n f ) time, where n f is the number of edges that bound the regions with the given land cover type. The approximation algorithm allows the square to be a factor 1+ε too large, and runs in O(n logn + n/ε 2 + n f log2 n f + (nlog2 n f )/( 2)) time. We also show how to compute largest clusters and outliers.


Land Cover Type Query Time Forest Inside Short Edge Point Pattern Analysis 
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. 1.
    Agarwal, P.K., de Berg, M., Matoušek, J., Schwarzkopf, O.: Constructing levels in arrangements and higher order Voronoi diagrams. SIAM J. Comput. 27, 654–667 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Agarwal, P.K., Erickson, J.: Geometric range searching and its relatives. In: Chazelle, B., Goodman, J.E., Pollack, R. (eds.) Advances in Discrete and Computational Geometry, Contemporary Mathematics, vol. 223, pp. 1–56. American Mathematical Society, Providence (1999)Google Scholar
  3. 3.
    Aggarwal, A., Imai, H., Katoh, N., Suri, S.: Finding k points with minimum diameter and related problems. J. Algorithms 12, 38–56 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Arora, S.: Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems. J. ACM 45(5), 753–782 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Chazelle, B., Edelsbrunner, H., Guibas, L.J., Sharir, M.: Algorithms for bichromatic line segment problems and polyhedral terrains. Algorithmica 11, 116–132 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chazelle, B., Guibas, L.J.: Fractional cascading: I. A data structuring technique. Algorithmica 1(3), 133–162 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)zbMATHGoogle Scholar
  8. 8.
    Datta, A., Lenhof, H.-P., Schwarz, C., Smid, M.: Static and dynamic algorithms for k-point clustering problems. J. Algorithms 19, 474–503 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications, 2nd edn. Springer, Berlin (2000)zbMATHGoogle Scholar
  10. 10.
    Eppstein, D., Erickson, J.: Iterated nearest neighbors and finding minimal polytopes. Discrete Comput. Geom. 11, 321–350 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Gudmundsson, J., van Kreveld, M., Narasimhan, G.: Region-restricted clustering for geographic data mining. Technical Report UU-CS-2006-031, Department of Information and Computing Sciences, Utrecht University (2006)Google Scholar
  12. 12.
    Han, J., Kamber, M.: Data Mining: Concepts and Techniques. Academic Press, San Diego (2001)Google Scholar
  13. 13.
    Har-Peled, S., Mazumdar, S.: Fast algorithms for computing the smallest k-enclosing circle. Algorithmica 41, 147–157 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Hartigan, J.A.: Clustering Algorithms. John Wiley & Sons, New York (1975)zbMATHGoogle Scholar
  15. 15.
    Jain, A.K., Dubes, R.C.: Algorithms for Clustering Data. Prentice Hall, Englewood Cliffs (1988)zbMATHGoogle Scholar
  16. 16.
    Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: A review. ACM Computing Surveys 31, 264–323 (1999)CrossRefGoogle Scholar
  17. 17.
    Koperski, K., Adhikary, J., Han, J.: Spatial data mining: Progress and challenges. In: Proc. SIGMOD 1996 Workshop on Research Issues on Data Mining and Knowledge Discovery (1996)Google Scholar
  18. 18.
    Lee, D.T.: On k-nearest neighbor Voronoi diagrams in the plane. IEEE Trans. Comput. C-31, 478–487 (1982)CrossRefGoogle Scholar
  19. 19.
    Miller, H.J., Han, J. (eds.): Geographic Data Mining and Knowledge Discovery. Taylor & Francis, London (2001)Google Scholar
  20. 20.
    O’Sullivan, D., Unwin, D.J.: Geographic Information Analysis. John Wiley & Sons, Hoboken (2003)Google Scholar
  21. 21.
    Roddick, J., Hornsby, K., Spiliopoulou, M.: An updated bibliography of temporal, spatial, and spatio-temporal data mining research. In: Roddick, J.F., Hornsby, K.S. (eds.) TSDM 2000. LNCS, vol. 2007, pp. 147–163. Springer, Heidelberg (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Joachim Gudmundsson
    • 1
  • Marc van Kreveld
    • 2
  • Giri Narasimhan
    • 3
  1. 1.National ICT Australia Ltd.SydneyAustralia
  2. 2.Dept. of Computer ScienceUtrecht UniversityThe Netherlands
  3. 3.Florida International UniversityMiamiUSA

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