Skip to main content
SpringerLink
Log in

Method of Fast Bandwidth Selection in a Nonparametric Classifier Corresponding to the a Posteriori Probability Maximum Criterion

  • Analysis and Synthesis of Signals and Images
  • Published:
Optoelectronics, Instrumentation and Data Processing Aims and scope

Abstract

A method of fast bandwidth selection in a nonparametric algorithm of pattern recognition corresponding to the maximum a posteriori probability criterion is proposed. The algorithm is based on the results of studying the asymptotic properties of the nonparametric estimate of the separation surface equation and probability densities in solving a two-alternative problem of pattern recognition. The proposed method is compared with the traditional approach based on minimizing the classification error probability estimate.

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. E. V. Dmitriev, V. V. Kozoderov, A. O. Dementyev, and A. N. Safonova, “Combining Classifiers in the Problem of Thematic Processing of Hyperspectral Aerospace Images,” Avtometriya 54(3), 3–13 (2018) [Optoelectron., Instrum. Data Process. 54 (3), 213–221 (2018)].

    Google Scholar 

  2. A. V. Lapko and V. A. Lapko, “Nonparametric Algorithms for Estimating the States of Natural Objects,” Avtometriya 54(5), 33–39 (2018) [Optoelectron., Instrum. Data Process. 54 (5), 451–456 (2018)].

    Google Scholar 

  3. M. I. Borrajo, W. González-Manteiga, and M. D. Martínez-Miranda, “Bandwidth Selection for Kernel Density Estimation with Length-Biased Data,” J. Nonparametr. Statist. 29(3), 636–668 (2017). DOI: https://doi.org/10.1080/10485252.2017.1339309.

    Article  MathSciNet  Google Scholar 

  4. S. Chen, “Optimal Bandwidth Selection for Kernel Density Functionals Estimation,” J. Probability Statist. 242683 (2015). DOI: https://doi.org/10.1155/2015/242683.

    Article  ADS  MathSciNet  Google Scholar 

  5. D. W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (John Wiley and Sons, New Jersey, 2015).

    Book  Google Scholar 

  6. S. J. Sheather, “Density Estimation,” Statist. Sci. 19(4), 588–597 (2004). DOI: https://doi.org/10.1214/088342304000000297.

    Article  MathSciNet  Google Scholar 

  7. B. W. Silverman, Density Estimation for Statistics and Data Analysis (Chapman and Hall, London, 1986).

    Book  Google Scholar 

  8. A. V. Lapko and V. A. Lapko, “Fast Algorithm for Choosing the Fuzziness Coefficients of the Kernel Functions in the Nonparametric Estimate of the Probability Density,” Izmer. Tekhnika, No. 6, 16–20 (2018). DOI: https://doi.org/10.32446/0368-1025it-2018-6-16-20.

  9. A. V. Lapko and V. A. Lapko, “Fast Algorithm for Choosing the Fuzziness Coefficients in Multi-Dimensional Kernel Estimates of the Probability Density,” Izmer. Tekhnika, No. 10, 19–23 (2018).

  10. A. V. Lapko and V. A. Lapko, Multilevel Nonparametric Systems of Information Processing (SibGAU, Krasnoyarsk, 2013) [in Russian].

    MATH  Google Scholar 

  11. E. Parzen, “On Estimation of a Probability Density Function and Mode,” Ann. Math. Statist. 33(3), 1065–1076 (1962).

    Article  ADS  MathSciNet  Google Scholar 

  12. V. A. Epanechnikov, “Nonparametric Estimate of the Multidimensional Probability Density,” Teor. Veroyatn. Primen. 14(1), 156–161 (1969).

    MathSciNet  MATH  Google Scholar 

  13. A. V. Lapko and V. A. Lapko, “Asymptotic Properties of the Nonparametric Estimate of the Separation Surface Equation in the Pattern Recognition Algorithm Corresponding to the Criterion of the Maximum a Posteriori Probability,” Sit. Upravl. Inform. Tekhnol. 42(4), 58–61 (2010).

    Google Scholar 

  14. V. E. Gmurman, Probability Theory and Mathematical Statistics (Vysshaya Shkola, Moscow, 1999) [in Russian].

    MATH  Google Scholar 

  15. A. S. Sharakshane, I. G. Zheleznov, and V. A. Ivnitskii, Complex Systems (Vysshaya Shkola, Moscow, 1977) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50, building 44, Krasnoyarsk, 660036, Russia

    A. V. Lapko & V. A. Lapko

  2. Reshetnev Siberian University of Science and Technology, pr. im. gazety “Krasnoyarskii rabochii” 31, Krasnoyarsk, 660037, Russia

    A. V. Lapko & V. A. Lapko

Authors
  1. A. V. Lapko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. A. Lapko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Lapko.

Additional information

Russian Text © The Author(s), 2019, published in Avtometriya, 2019, Vol. 55, No. 6, pp. 76–86.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lapko, A.V., Lapko, V.A. Method of Fast Bandwidth Selection in a Nonparametric Classifier Corresponding to the a Posteriori Probability Maximum Criterion. Optoelectron.Instrument.Proc. 55, 597–605 (2019). https://doi.org/10.3103/S8756699019060104

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S8756699019060104

Keywords

Search

Navigation