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Method of Constructing a Nonlinear Approximating Scheme of a Complex Signal: Application Pattern Recognition

Author

Listed:
  • Oksana Mandrikova

    (Institute of Cosmophysical Research and Radio Wave Propagation, Far Eastern Branch of the Russian Academy of Sciences, Mirnaya st, 7, Paratunka, 684034 Kamchatskiy Kray, Russia)

  • Bogdana Mandrikova

    (Institute of Cosmophysical Research and Radio Wave Propagation, Far Eastern Branch of the Russian Academy of Sciences, Mirnaya st, 7, Paratunka, 684034 Kamchatskiy Kray, Russia)

  • Anastasia Rodomanskay

    (Institute of Cosmophysical Research and Radio Wave Propagation, Far Eastern Branch of the Russian Academy of Sciences, Mirnaya st, 7, Paratunka, 684034 Kamchatskiy Kray, Russia)

Abstract

A method for identification of structures of a complex signal and noise suppression based on nonlinear approximating schemes is proposed. When we do not know the probability distribution of a signal, the problem of identifying its structures can be solved by constructing adaptive approximating schemes in an orthonormal basis. The mapping is constructed by applying threshold functions, the parameters of which for noisy data are estimated to minimize the risk. In the absence of a priori information about the useful signal and the presence of a high noise level, the use of the optimal threshold is ineffective. The paper introduces an adaptive threshold, which is assessed on the basis of the posterior risk. Application of the method to natural data has confirmed its effectiveness.

Suggested Citation

  • Oksana Mandrikova & Bogdana Mandrikova & Anastasia Rodomanskay, 2021. "Method of Constructing a Nonlinear Approximating Scheme of a Complex Signal: Application Pattern Recognition," Mathematics, MDPI, vol. 9(7), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:737-:d:526026
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    Citations

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    Cited by:

    1. Oksana Mandrikova & Yuryi Polozov & Nataly Zhukova & Yulia Shichkina, 2022. "Approximation and Analysis of Natural Data Based on NARX Neural Networks Involving Wavelet Filtering," Mathematics, MDPI, vol. 10(22), pages 1-16, November.
    2. Oksana Mandrikova & Bogdana Mandrikova & Oleg Esikov, 2023. "Detection of Anomalies in Natural Complicated Data Structures Based on a Hybrid Approach," Mathematics, MDPI, vol. 11(11), pages 1-17, May.

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