Skip to main content

Prototype Extraction for k-NN Classifiers using Median Strings

  • Chapter
Pattern Recognition and String Matching

Part of the book series: Combinatorial Optimization ((COOP,volume 13))

  • 448 Accesses

Abstract

The k-Nearest Neighbour rule is one of the most popular non-parametric classification techniques in Pattern Recognition. This technique requires a set of good prototypes to represent pattern classes. One possibility is to define the given training set as the set of prototypes. Obviously, this approach presents a high computational cost if the training set is large. Alternatively, clustering techniques allow for the description of a training corpus in terms of clusters. A cluster is formed by patterns with certain simmilarities [1]. These clusters can be represented by a set of prototypes. The selection of adequate prototypes is one of the most important problems in Pattern Recognition.

This work was partially supported by the Spanish MCT under projects TIC2000-1703-C03-01 and TIC2000-1599-CO2-01.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. O. Duda, P. Hart, and D. G. Stork, Pattern Classification, (John Wiley, 2001 ).

    MATH  Google Scholar 

  2. D. L. Wilson, Asymptotic properties of nearest neighbour rules using edited data, IEEE Transactions on Systems, Man and Cybernetics, 2 (1972) pp. 408–421.

    Article  MATH  Google Scholar 

  3. P. Devijver and J. Kittler, Pattern Recognition: A Statistical Approach. Prentice Hall, Inc., London, 1982.

    MATH  Google Scholar 

  4. P. E. Hart, The condensed nearest neighbour rule, IEEE Transactions on Information Theory, 14 (1968), pp. 515–516.

    Article  Google Scholar 

  5. Fu, K. S., 1982. Syntactic Pattern Recognition. Prentice-Hall.

    MATH  Google Scholar 

  6. C. de la Higuera and F. Casacuberta, The topology of strings: two npcomplete problems, Theoretical Computer Science 230 (2000) pp. 39–48.

    Article  MATH  MathSciNet  Google Scholar 

  7. T. Kohonen, Median strings, Pattern Recognition Letters 3 (1985) pp. 309–313.

    Article  Google Scholar 

  8. F. Kruzslicz, A greedy algorithm to look for median strings, in: Abstracts of the Conference on PhD Students in Computer Science, (Institute of informatics of the József Attila University, 1988 ).

    Google Scholar 

  9. I. Fischer and A. Zell, String averages and self-organizing maps for strings, in: Proceeding of the Second ICSC Symposium on Neural Computation, (2000) pp. 208–215.

    Google Scholar 

  10. X. Jiang, A. Munger, and H. Bunke, On Median Graphs: Properties, Algorithms, and Applications, IEEE Transactions on Pattern Analysis and Machine Intelligence 23 (10) (2001) pp. 1144–1151.

    Article  Google Scholar 

  11. F. Casacuberta and M. de Antonio, A greedy algorithm for computing approximate median strings, in: Proceedings of the VII Simposium Nacional de Reconocimiento de Formas y Ancálisis de Imdgenes, (1997) pp. 193–198.

    Google Scholar 

  12. C. D. Martínez, A. Juan and F. Casacuberta, Use of Median String for Classification, in: Proceedings of the 15th International Conference on Pattern Recognition, (Vol. 2, Barcelona, Spain, 2000 ) pp. 907–910.

    Google Scholar 

  13. C. Martínez, A. Juan and F. Casacuberta, Improving classification using median string and nn rules, in: Proceedings of IX Simposium Nacional de Reconocimiento de Formas y Andlisis de Imcágenes, (2001) pp. 391–394.

    Google Scholar 

  14. R. Wagner and M. Fisher, The string-to-string correction problem. Journal of the ACM21 (1974) pp. 168–178.

    Article  MATH  Google Scholar 

  15. E. Vidal, A. Marzal and P. Aibar, Fast computation of normalized edit distances, IEEE Transactions on Pattern Analysis and Machine Intelligence 17 (9) (1995) pp. 899–902.

    Article  Google Scholar 

  16. A. Juan, and E. Vidal, On the Use of Edit Distances and an Efficient k-NN Search Technique (k-AESA) for Fast and Accurate String Classification, in: Proceedings of the 15th International Conference on Pattern Recognition, (Vol. 2, Barcelona, Spain, 2000 ) pp. 680–683.

    Google Scholar 

  17. C. Lundsteen, J. Philip and E. Granum, Quantitative Analysis of 6895 Digitized Trypsin G-banded Human Metaphase Chromosomes, Clinical Genetics 18 (1980) pp. 355–370.

    Article  Google Scholar 

  18. E. Granum and M. Thomason, Automatically Inferred Markov Network Models for Classification of Chromosomal Band Pattern Structures, Cytometry 11 (1990) pp. 26–39.

    Article  Google Scholar 

  19. J. Gregor and M. G. Thomason, A Disagreement Count Scheme for Inference of Constrained Markov Networks, in: L. Miclet and C. de la Higuera (Eds.), Grammatical Inference: Learning Syntax from Sentences, (Vol. 1147 of Lecture Notes in Computer Science, Springer, 1996 ) pp. 168–178.

    Chapter  Google Scholar 

  20. E. Vidal, and M. J. Castro, Classification of Banded Chromosomes using Error-Correcting Grammatical Inference (ECGI) and Multilayer Perceptron (MLP), in: Proceedings of the VII Simposium Nacional de Reconocimiento de Formas y Anc lisis de Imc genes, (Vol. 1, Bellaterra, Spain, 1997 ) pp. 31–36.

    Google Scholar 

  21. E. Vidal, M. J. Castro and J. A. Sanchez, Classification of Banded Chromosomes, (tech. rep., DSIC, Universidad Politécnica de Valencia, Spain ) 1997.

    Google Scholar 

  22. C. D. Martínez-Hinarejos, A. Juan, F. Casacuberta, Median String for k-Nearest Neighbour classification, Pattern Recognition Letters, acepted for revision.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Kluwer Academic Publishers

About this chapter

Cite this chapter

Martínez-Hinarejos, C.D., Juan, A., Casacuberta, F. (2003). Prototype Extraction for k-NN Classifiers using Median Strings. In: Chen, D., Cheng, X. (eds) Pattern Recognition and String Matching. Combinatorial Optimization, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0231-5_18

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-0231-5_18

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7952-2

  • Online ISBN: 978-1-4613-0231-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics