Using Rough Sets and Maximum Similarity Graphs for Nearest Prototype Classification

  • Yenny Villuendas-Rey
  • Yailé Caballero-Mota
  • María Matilde García-Lorenzo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7441)


The nearest neighbor rule (NN) is one of the most powerful yet simple non parametric classification techniques. However, it is time consuming and it is very sensitive to noisy as well as outlier objects. To solve these deficiencies several prototype selection methods have been proposed by the scientific community. In this paper, we propose a new editing and condensing method. Our method combines the Rough Set theory and the Compact Sets structuralizations to obtain a reduced prototype set. Numerical experiments over repository databases show the high quality performance of our method according to classifier accuracy.


nearest neighbor prototype selection editing methods 


  1. 1.
    Triguero, I., Derrac, J., García, S., Herrera, F.: A taxonomy and Experimental Study on prototype generation for Nearest Neighbor classification. IEEE Transactions on Systems, Man, and Cybernetics (2012), doi:10.1109/TSMCC.2010.2103939Google Scholar
  2. 2.
    Dasarathy, B.D.: Minimal consistent set (MCS) identification for optimal nearest neighbor decision systems design. IEEE Transactions on Systems, Man and Cybernetics 24, 511–517 (1994)CrossRefGoogle Scholar
  3. 3.
    Chou, C.H., Kuo, B.A., Cheng, F.: The Generalized Condensed Nearest Neighbor rule as a data reduction technique. In: 18th International Conference on Pattern Recognition, pp. 556–559 (2006)Google Scholar
  4. 4.
    Olvera-López, J.A., Carrasco-Ochoa, J.A., Martínez-Trinidad, J.F.: Prototype Selection Via Prototype Relevance. In: Ruiz-Shulcloper, J., Kropatsch, W.G. (eds.) CIARP 2008. LNCS, vol. 5197, pp. 153–160. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Huang, C.-C.: A novel gray-based reduced NN classification method. Pattern Recognition 39, 1979–1986 (2006)zbMATHCrossRefGoogle Scholar
  6. 6.
    García-Borroto, M., Villuendas-Rey, Y., Carrasco-Ochoa, J.A., Martínez-Trinidad, J.F.: Finding Small Consistent Subset for the Nearest Neighbor Classifier Based on Support Graphs. In: Bayro-Corrochano, E., Eklundh, J.-O. (eds.) CIARP 2009. LNCS, vol. 5856, pp. 465–472. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Zafra, A., Gibaja, E.L., Ventura, S.: Multiple instance learning with multiple objective genetic programming for web mining. Applied Soft Computing 11, 93–102 (2011)CrossRefGoogle Scholar
  8. 8.
    Nikolaidis, K., Goulemas, J.Y., Wu, Q.H.: A class boundary preserving algorithm for data condensation. Pattern Recognition 44, 704–715 (2011)zbMATHCrossRefGoogle Scholar
  9. 9.
    Wilson, D.L.: Asymptotic properties of nearest neighbor rules using edited data. IEEE Transactions on Systems, Man and Cybernetics SMC-2, 408–421 (1972)Google Scholar
  10. 10.
    Hattori, K., Takanashi, M.: A new edited k-nearest neighbor rule in the pattern classification problem. Pattern Recognition 33, 521–528 (2000)CrossRefGoogle Scholar
  11. 11.
    Caballero, Y., Bello, R., Salgado, Y., García, M.M.: A method to edit training set based on rough sets. International Journal of Computational Intelligence Research 3, 219–229 (2007)CrossRefGoogle Scholar
  12. 12.
    García-Borroto, M., Villuendas-Rey, Y., Carrasco-Ochoa, J.A., Martínez-Trinidad, J.F.: Using Maximum Similarity Graphs to Edit Nearest Neighbor Classifiers. In: Bayro-Corrochano, E., Eklundh, J.-O. (eds.) CIARP 2009. LNCS, vol. 5856, pp. 489–496. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Pawlak, Z.: Rough Sets. International Journal of Information & Computer Sciences 11, 341–356 (1982)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Ruiz-Shulcloper, J., Abidi, M.A.: Logical combinatorial pattern recognition: A Review. In: Pandalai, S.G. (ed.) Recent Research Developments in Pattern Recognition. Transword Research Networks, USA, pp. 133–176 (2002)Google Scholar
  15. 15.
    Hu, Q., Yu, D., Liu, J., Wu, C.: Neighborhood rough sets based heterogeneous feature selection. Information Sciences 178, 3577–3594 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Merz, C.J., Murphy, P.M.: UCI Repository of Machine Learning Databases. University of California at Irvine, Department of Information and Computer Science, Irvine (1998)Google Scholar
  17. 17.
    Wilson, R.D., Martinez, T.R.: Improved Heterogeneous Distance Functions. Journal of Artificial Intelligence Research 6, 1–34 (1997)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yenny Villuendas-Rey
    • 1
    • 3
  • Yailé Caballero-Mota
    • 2
  • María Matilde García-Lorenzo
    • 3
  1. 1.Computer Science DepartmentUniversity of Ciego de ÁvilaCuba
  2. 2.Computer Science DepartmentUniversity of CamagüeyCuba
  3. 3.Computer Science DepartmentUniversity of Las VillasCuba

Personalised recommendations