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Using the Dual of Proximity Graphs for Binary Decision Tree Design

  • J. S. Sánchez
  • F. Pla
  • M. C. Herrero
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1876)

Abstract

This paper describes an algorithm to design a tree-structured classifier with the hyperplanes associated with a set of prototypes. The main purpose of this technique consists of defining a classification scheme whose result is close to that produced by the Nearest Neighbour decision rule, but getting important computation savings during classification.

Keywords

Nearest Neighbour Decision Tree Classification GabrielGraph Relative Neighbourhood Graph 

References

  1. 1.
    S. O. Belkasim, M. Shridhar and M. Ahmadi, “Pattern classification using an efficient KNNR”, Pattern Recognition 25, 1269–1274, 1992.CrossRefGoogle Scholar
  2. 2.
    N. K. Bose and A. K. Garga, “Neural network design using Voronoi diagrams”, IEEE Trans. on Neural Networks 4, 778–787, 1993.CrossRefGoogle Scholar
  3. 3.
    L. Breiman, J. H. Friedman, R. A. Olshen and C. J. Stone, Classification and regression trees, Chapman & Hall: New York, 1984.zbMATHGoogle Scholar
  4. 4.
    C. L. Chang, “Finding prototypes for nearest neighbor classifiers”, IEEE Trans. on Computers 23, 1179–1184, 1974.zbMATHCrossRefGoogle Scholar
  5. 5.
    C. H. Chen and A. Józwik, “A sample set condensation algorithm for the class sensitive artificial neural network”, Pattern Recognition Letters 17, 819–823, 1996.CrossRefGoogle Scholar
  6. 6.
    T. M. Cover and P. E. Hart, “Nearest neighbor pattern classification”, IEEE Trans. on Information Theory 13, 21–27, 1967.zbMATHCrossRefGoogle Scholar
  7. 7.
    P. A. Devijver and J. Kittler, Pattern recognition: a statistical approach, Prentice Hall: Englewood Cliffs, NJ, 1982.zbMATHGoogle Scholar
  8. 8.
    A. Djouadi and E. Bouktache, “A fast algorithm for the nearest-neighbor classifier”, IEEE Trans. on Pattern Analysis and Machine Intelligence 19, 277–282, 1997.CrossRefGoogle Scholar
  9. 9.
    J. H. Friedman, J. L. Bentley and R. A. Finkel, “An algorithm for finding best matches in logarithmic expected time”, ACM Trans. on Math. Software 3, 209–226, 1977.zbMATHCrossRefGoogle Scholar
  10. 10.
    K. Fukunaga and P. M. Narendra, “A branch and bound algorithm for computing k-nearest neighbors”, IEEE Trans. on Computers 24, 750–753, 1975.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    P. J. Grother, G. T. Candela and J. L. Blue, “Fast implementations of nearest neighbour classifiers”, Pattern Recognition 30, 459–465, 1997.CrossRefGoogle Scholar
  12. 12.
    P. E. Hart, “The condensed nearest neighbor rule”, IEEE Trans. on Information Theory 14, 515–516, 1968.CrossRefGoogle Scholar
  13. 13.
    D. Heath, S. Kasif and S. Salzberg, “Learning oblique decision trees”, In Proc. 13th Int. Joint Conf. Artfificial Intelligence, 1202–1207, 1993.Google Scholar
  14. 14.
    J.W. Jaromczyk and G.T. Toussaint, “Relative neighborhood graphs and their relatives”, Proc. IEEE 80, 1502–1517, 1992.CrossRefGoogle Scholar
  15. 15.
    T. Kohonen, “The self-organizing map”, Proc. IEEE 9, 1464–1480, 1990.CrossRefGoogle Scholar
  16. 16.
    O. J. Murphy, “Nearest neighbor pattern classification perceptrons”, Proc. IEEE, 78, 1595–1598, 1990.CrossRefGoogle Scholar
  17. 17.
    F.P. Preparata and M.I. Shamos, Computational geometry. An introduction, Springer: New York, 1985.Google Scholar
  18. 18.
    J. R. Quinlan, “Induction of decision trees”, Machine Learning 1, 81–106, 1986.Google Scholar
  19. 19.
    G. L. Ritter, H. B. Woodruff, S. R. Lowry and T. L. Isenhour, “An algorithm for a selective nearest neighbour decision rule”, IEEE Trans. on Information Theory 21, 665–669, 1975.zbMATHCrossRefGoogle Scholar
  20. 20.
    J.S. Sánchez, F. Pla and F.J. Ferri, “On the use of neighbourhood-based nonparametric classifiers”, Pattern Recognition Letters 18, 1179–1186, 1997.CrossRefGoogle Scholar
  21. 21.
    J.S. Sánchez, F. Pla and F.J. Ferri, “A Voronoi-diagram-based approach to oblique decision tree induction”, In Proc. 14th Int. Conf. Pattern Recognition 1, 542–544, 1998.Google Scholar
  22. 22.
    G. T. Toussaint, B. K. Bhattacharya and R. S. Poulsen, “The application of Voronoi diagrams to nonparametric decision rules”, In Computer Science & Statistics: 16th Symp. Interface, 97–108, 1984.Google Scholar
  23. 23.
    E. Vidal, “An algorithm for finding nearest neighbours in (approximately) constant average time”, Pattern Recognition Letters 4, 145–157, 1986.CrossRefGoogle Scholar
  24. 24.
    H. Yan, “Prototype optimization for nearest neighbor classifiers using a two-layer perceptron”, Pattern Recognition 26, 317–324, 1993.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • J. S. Sánchez
    • 1
  • F. Pla
    • 1
  • M. C. Herrero
    • 1
  1. 1.Departament d’InformàticaUniversitat Jaume ICastellóSpain

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