Using the Geometrical Distribution of Prototypes for Training Set Condensing

  • María Teresa Lozano
  • José Salvador Sánchez
  • Filiberto Pla
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3040)


In this paper, some new approaches to training set size reduction are presented. These schemes basically consist of defining a small number of prototypes that represent all the original instances. Although the ultimate aim of the algorithms proposed here is to obtain a strongly reduced training set, the performance is empirically evaluated over nine real datasets by comparing the reduction rate and the classification accuracy with those of other condensing techniques.


Voronoi Diagram Near Neighbour Decision Boundary Geometrical Distribution Pattern Recognition Letter 
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.
    Aha, D.W., Kibler, D., Albert, M.K.: Instance-based learning algorithms. Machine Learning 6(1), 37–66 (1991)Google Scholar
  2. 2.
    Ainslie, M.C., Sánchez, J.S.: Space partitioning for instance reduction in lazy learning algorithms. In: 2nd Workshop on Integration and Collaboration Aspects of Data Mining, Decision Support and Meta-Learning, pp. 13–18 (2002)Google Scholar
  3. 3.
    Chang, C.L.: Finding prototypes for nearest neighbor classifiers. IEEE Trans. on Computers 23, 1179–1184 (1974)zbMATHCrossRefGoogle Scholar
  4. 4.
    Charnes, A., Cooper, W., Rhodes, E.: Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Chaudhuri, B.B.: A new definition of neighbourhood of a point in multi-dimensional space. Pattern Recognition Letters 17, 11–17 (1996)CrossRefGoogle Scholar
  6. 6.
    Chen, C.H., Józwik, A.: A sample set condensation algorithm for the class sensitive artificial neural network. Pattern Recognition Letters 17, 819–823 (1996)CrossRefGoogle Scholar
  7. 7.
    Dasarathy, B.V.: Nearest neighbor (NN) norms: NN pattern classification techniques. IEEE Computer Society Press, Los Alamitos (1990)Google Scholar
  8. 8.
    Dasarathy, B.V.: Minimal consistent subset (MCS) identification for optimal nearest neighbor decision systems design. IEEE Trans. on Systems, Man, and Cybernetics 24, 511–517 (1994)CrossRefGoogle Scholar
  9. 9.
    Devijver, P.A., Kittler, J.: Pattern Recognition: A Statistical Approach. Prentice Hall, Englewood Cliffs (1982)zbMATHGoogle Scholar
  10. 10.
    Hart, P.: The condensed nearest neighbor rule. IEEE Trans. on Information Theory 14, 505–516 (1968)CrossRefGoogle Scholar
  11. 11.
    Merz, C. J., Murphy, P.M.: UCI Repository of Machine Learning Databases. Dept. of Information and Computer Science, U. of California, Irvine, CA (1998) Google Scholar
  12. 12.
    Sánchez, J.S., Pla, F., Ferri, F.J.: On the use of neighbourhood-based nonparametric classifiers. Pattern Recognition Letters 18, 1179–1186 (1997)CrossRefGoogle Scholar
  13. 13.
    Tomek, I.: Two modifications of CNN. IEEE Transactions on Systems, Man and Cybernetics, SMC-6, 769–772 (1976)Google Scholar
  14. 14.
    Toussaint, G.T., Bhattacharya, B.K., Poulsen, R.S.: The application of Voronoi diagrams to nonparametric decision rules. In: Billard, L. (ed.) Computer Science and Statistics: The Interface, Elsevier Science, North-Holland, Amsterdam (1985)Google Scholar
  15. 15.
    Wilson, D.L.: Asymptotic properties of nearest neighbor rules using edited data sets. IEEE Trans. on Systems, Man and Cybernetics 2, 408–421 (1972)zbMATHCrossRefGoogle Scholar
  16. 16.
    Wilson, D.R., Martinez, T.R.: Reduction techniques for instance-based learning algorithms. Machine Learning 38, 257–286 (2000)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • María Teresa Lozano
    • 1
  • José Salvador Sánchez
    • 1
  • Filiberto Pla
    • 1
  1. 1.Dept. Lenguajes y Sistemas InformáticosUniversitat Jaume I, Campus Riu SecCastellónSpain

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