Skip to main content
SpringerLink
Log in

Statistical Complexity as a Criterion for the Useful Signal Detection Problem

  • OPTIMIZATION, SYSTEM ANALYSIS, AND OPERATIONS RESEARCH
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants of statistical complexity are obtained analytically and conclusions about the efficiency of using one or another variant for detection problem are made. The comparison of considered information characteristics is shown and analytical results are illustrated on an example of synthesized signals. A method is proposed for selecting the threshold of the information criterion, which can be used in decision rule for useful signal detection in the signal-noise mixture. The choice of the threshold depends a priori on the analytically obtained maximum values. As a result, the complexity based on the total variation demonstrates the best ability of useful signal detection.

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

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.

REFERENCES

  1. Shannon, C.E., A Mathematical Theory of Communication, Bell Syst. Tech. J., 1948, vol. 27, pp. 379–423.

    Article  MathSciNet  MATH  Google Scholar 

  2. Gray, R.M., Entropy and Information Theory, New York: Springer, 2011. https://doi.org/10.1007/978-1-4419-7970-4

  3. Holub, A., Perona, P., and Burl, M.C., Entropy-based Active Learning for Object Recognition, Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), IEEE, 2008, pp. 1–8. https://doi.org/10.1109/CVPRW.2008.4563068

  4. Osisanwo, F.Y., Akinsola, J.E.T., Awodele, O., et al., Supervised Machine Learning Algorithms: Classification and Comparison, Int. J. Comput. Trends Technol. (IJCTT), 2017, vol. 48, no. 3, pp. 128–138. https://doi.org/10.14445/22312803/IJCTT-V48P126

    Article  Google Scholar 

  5. Shen, J., Hung, J., and Lee, L., Robust Entropy-based Endpoint Detection for Speech Recognition in Noisy Environments, Proc. 5th International Conference on Spoken Language Processing (ICSLP), 1998. https://doi.org/10.21437/icslp.1998-527

  6. Ribeiro, M., Henriques, T., Castro, L., Souto, A., Antunes, L., Costa-Santos, C., and Teixeira, A., The Entropy Universe, Entropy, 2021, vol. 23, no. 2, p. 222. https://doi.org/10.3390/e23020222

    Article  MathSciNet  Google Scholar 

  7. Ramirez, J., Segura, J.C., Benitez, C., et al., A New Kullback-Leibler VAD for Speech Recognition in Noise, IEEE Signal Proc. Lett., 2004, vol. 11, no. 2, pp. 266–269. https://doi.org/10.1109/LSP.2003.821762

    Article  Google Scholar 

  8. Horie, T., Burioka, N., Amisaki, T., and Shimizu, E., Sample Entropy in Electrocardiogram During Atrial Fibrillation, Yonago Acta Medica, 2018, vol. 61, no. 1, pp. 49–57. https://doi.org/10.33160/yam.2018.03.007

    Article  Google Scholar 

  9. Lamberti, P.W., Martin, M.T., Plastino, A., and Rosso, O.A., Intensive Entropic Non-TrivialityMeasure, Phys. A: Stat. Mech. Appl., 2004, vol. 334, no. 1, pp. 119–131. https://doi.org/10.1016/j.physa.2003.11.005

    Article  Google Scholar 

  10. Lopez-Ruiz, R., Shannon Information, LMC Complexity and Renyi Entropies: A Straightforward Approach, Biophys. Chem., 2005, vol. 115, no. 3, pp. 215–218. https://doi.org/10.1016/j.bpc.2004.12.035

    Article  Google Scholar 

  11. Zunino, L., Soriano, M.C., and Rosso, O.A., Distinguishing Chaotic and Stochastic Dynamics from Time Series by Using a Multiscale Symbolic Approach, Phys. Rev. E. Stat. Nonlin. Soft. Matter Phys., 2012, vol. 86, no. 4, pp. 1–5. https://doi.org/10.1103/PhysRevE.86.046210

    Article  Google Scholar 

  12. Ronald, L.A. and Duncan, W.M., Signal Analysis: Time, Frequency, Scale, and Structure, New Jersey: IEEE Press, 2004.

    Google Scholar 

  13. Shiryaev, A.N., Veroyatnostno-statisticheskie metody v teorii prinyatiya reshenii (Probabilistic-Statistical Methods in Decision-Making Theory), Moscow: MTSNMO: NMU, 2020.

  14. Kishan, G.M., Chilukuri, K.M., and HuaMing Huang, Anomaly Detection Principles and Algorithms, Cham: Springer, 2017. https://doi.org/10.1007/978-3-319-67526-8

  15. Berlin, L.M., Galyaev, A.A., and Lysenko, P.V., Comparison of Information Criteria for Detection of Useful Signals in Noisy Environments, Sensors, 2023, vol. 23, no. 4, p. 2133. https://doi.org/10.3390/s23042133

    Article  Google Scholar 

  16. Johnson, P., Moriarty, J., and Peskir, G., Detecting Changes in Real-Time Data: A User’s Guide to Optimal Detection, Philos. Trans. Royal Soc. A, 2017, vol. 375, p. 16, p. 2100. https://doi.org/10.1098/rsta.2016.0298

  17. Li, Z., Li, Y., and Zhang, K.A., Feature ExtractionMethod of Ship-Radiated Noise Based on Fluctuation-Based Dispersion Entropy and Intrinsic Time-Scale Decomposition, Entropy, 2019, vol. 21, no. 7, p. 693. https://doi.org/10.3390/e21070693

    Article  Google Scholar 

  18. Sason, I., On f-Divergences: Integral Representations, Local Behavior, and Inequalities, Entropy, 2018, vol. 20, no. 5, p. 383. https://doi.org/10.3390/e20050383

    Article  MathSciNet  Google Scholar 

Download references

Funding

This work was supported by the Russian Scientific Foundation, project no. 23-19-00134.

Author information

Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    A. A. Galyaev, P. V. Lysenko & L. M. Berlin

Authors
  1. A. A. Galyaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. V. Lysenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. M. Berlin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. A. Galyaev, P. V. Lysenko or L. M. Berlin.

Additional information

This paper was recommended for publication by A.V. Nazin, a member of the Editorial Board

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Galyaev, A.A., Lysenko, P.V. & Berlin, L.M. Statistical Complexity as a Criterion for the Useful Signal Detection Problem. Autom Remote Control 84, 753–771 (2023). https://doi.org/10.1134/S0005117923070056

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117923070056

Keywords:

Search

Navigation