Skip to main content
SpringerLink
Log in

Synthesis of systems of neurofunctional transformations in classification problems

  • Systems Analysis
  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

Optimal synthesis of linear and nonlinear transformations is used to synthesize pattern recognition systems. The necessary and sufficient conditions for the existence of robust dichotomous linear separability of sets in feature space are represented in terms of pseudoinverse operations. The synthesis of classification systems is reduced to searching for the best nonlinear transformations of the components of the feature vector or optimal linear combinations of its components.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. Kohonen, Self-Organizing Maps, 3rd ed., Springer, Tokyo (2001).

    MATH  Google Scholar 

  2. V. N. Vapnik, Statistical Learning Theory, Wiley, New York (1998).

    MATH  Google Scholar 

  3. S. Haykin, Neural Networks, A Comprehensive Foundation, Prentice Hall, Upper Saddle River (NJ) (1999).

    MATH  Google Scholar 

  4. A. G. Ivakhnenko, Self-Organizing Systems of Recognition and Automatic Control [in Russian], Tekhnika, Kyiv (1969).

    Google Scholar 

  5. N. M. Kussul’, A. Yu. Shelestov, and A. M. Lavrinyuk, Intelligent Calculations: A Textbook [in Ukrainian], Naukova Dumka, Kyiv (2006).

    Google Scholar 

  6. N. F. Kirichenko, “Analytical representation of perturbations of pseudoinverse matrices,” Cybern. Syst. Analysis, 33, No. 2, 230–238 (1997).

    Article  MATH  Google Scholar 

  7. N. F. Kirichenko and N. P. Lepekha, “Application of pseudoinverse and projective matrices to studying control, observation, and identifications problems,” Cybern. Syst. Analysis, 38, No. 4, 568–585 (2002).

    Article  MATH  Google Scholar 

  8. N. F. Kirichenko, Yu. V. Krak, and A. A. Polishchuk, “Pseudoinverse and projection matrices in problems of synthesis of functional transformers,” Cybern. Syst. Analysis, 40, No. 3, 407–419 (2004).

    Article  MATH  Google Scholar 

  9. N. F. Kirichenko, V. S. Donchenko, and D. P. Serbaev, “Nonlinear recursive regression transformers: Dynamic systems and optimization,” Cybern. Syst. Analysis, 41, No. 3, 364–373 (2005).

    Article  MATH  Google Scholar 

  10. A. Albert, Regression, Pseudoinversion, and Recurrent Estimation [Russian translation], Nauka, Moscow (1977).

    Google Scholar 

  11. N. F. Kirichenko, A. M. Reznik, and S. P. Shchetenyuk, “Matrix pseudoinversion in the problem of design of associative memory,” Cybern. Syst. Analysis, 37, No. 3, 308–316 (2001).

    Article  MATH  Google Scholar 

  12. I. N. Bronshtein and K. A. Semendyaev, A Handbook of Mathematics [in Russian], Gos. Izd. Tekhn.-Teoret. Lit., Moscow (1956).

    Google Scholar 

  13. Yu. S. Zav’yalov, B. I. Kvasov, and V. L. Miroshnichenko, Methods of Spline Functions [in Russian], Nauka, Moscow (1980).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    N. F. Kirichenko & Yu. G. Krivonos

  2. Taras Shevchenko National University, Kyiv, Ukraine

    N. P. Lepekha

Authors
  1. N. F. Kirichenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. G. Krivonos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. P. Lepekha
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 47–56, May–June 2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kirichenko, N.F., Krivonos, Y.G. & Lepekha, N.P. Synthesis of systems of neurofunctional transformations in classification problems. Cybern Syst Anal 43, 353–361 (2007). https://doi.org/10.1007/s10559-007-0056-4

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-007-0056-4

Keywords

Search

Navigation