Measure of Similarity and Compactness in Competitive Space

  • Nikolay Zagoruiko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5772)

Abstract

The given work is devoted to measures of similarity which are used at discovering of empirical regularities (knowledge). The function of competitive (rival) similarity (FRiS) is proposed as a similarity measure for classification and pattern recognition applications. This function allows one to design effective algorithms for solving all basic data mining tasks, obtain quantitative estimates of the compactness of patterns and the informativeness of feature spaces, and construct easily interpretable decision rules. The method is suitable for any number of patterns regardless of the nature of their distributions and conditionality of training samples (the ratio of the numbers of objects and features). The usefulness of the FRiS is shown by solving a problems of molecular biology.

Keywords

similarity measure pattern recognition compactness informativeness 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Voronin, Ju.A.: The beginnings of the theory of similarity. Edition by Computer Centre of the Siberian Branch of the Russian Academy of Science, Novosibirsk (1989) (in Russian)Google Scholar
  2. 2.
    Shrejder, J.A.: Equality, similarity and order. ”Science”, M (1971) (in Russian)Google Scholar
  3. 3.
    Fix, E., Hodges, J.: Discriminatory Analysis: Nonparametric Discrimination: Consistency Properties. Technical report, USAF School of Aviation Med. Randolph Field, TX, Rep. 21-49-004 (1951)Google Scholar
  4. 4.
    Kira, K., Rendell, L.: The Feature Selection Problem: Traditional Methods and a New Algorithm. In: Proc. 10th Nat’l Conf. Artificial Intelligence (AAAI 1992), pp. 129–134 (1992)Google Scholar
  5. 5.
    Zagoruiko, N.G., Borisova, I.A., Dyubanov, V.V., Kutnenko, O.A.: Methods of Recognition Based on the Function of Rival Similarity. Pattern Recognition and Image Analysis 18(1), 1–6 (2008)CrossRefMATHGoogle Scholar
  6. 6.
    Braverman, E.M.: Experiences on training the machine to recognition of visual patterns. Automatics and Telemechanics 23(3), 349–365 (1962) (in Russian)Google Scholar
  7. 7.
    Vorontsov, K.V., Koloskov, A.O.: Profiles of compactness and allocation of basic objects in metric algorithms of classification. The Artificial intellect (2006) (in Russian)Google Scholar
  8. 8.
    Fisher, R.: The use of multiple measurements in taxonomic problems. Ann. Eugen. (7), 79–188 (1936)Google Scholar
  9. 9.
    Guy, I., Weston, J., Barnhill, S., Vapnik, V.: Gene Selection for Cancer Classification using Support Vector Machines. Machine Learning 46(1-3), 389–422 (2002)MATHGoogle Scholar
  10. 10.
  11. 11.
    Merill, T., Green, O.M.: On the effectiveness of receptions in recognition systems. IEEE Trans. Inform. Theory IT-9, 11–17 (1963)CrossRefGoogle Scholar
  12. 12.
    Zagoruiko, N.G., Kutnenko, O.A., Ptitsin, A.A.: Algorithm GRAD for Selection of Informative Genetic Feature. In: Proc. Int. Conf. on Computational Molecular Biology, Moscow, pp. 8–9 (2005)Google Scholar
  13. 13.
    Zagoruiko, N.G., Kutnenko, O.A.: Recognition Methods Based on the AdDel Algorithm. Int. Journal “Pattern Recognition and Image Analysis” 14(2), 198–204 (2004)MATHGoogle Scholar
  14. 14.
  15. 15.
    Adam, B.L., Qu, Y., Davis, J.W., et al.: Serum protein fingerprinting coupled with a pattern- matching algorithm distinguishes prostate cancer from benign prostate hyperplasia and healthy men. Cancer Res. 62, 3609–3614 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Nikolay Zagoruiko
    • 1
  1. 1.Institute of Mathematics of the Siberian Devision, of the Russian Academy of SciencesNovosibirskRussia

Personalised recommendations