Skip to main content
SpringerLink
Log in

Tracking the states of a nonlinear and nonstationary system in the weight-space of artificial neural networks

  • ORIGINAL ARTICLE
  • Published:
Medical and Biological Engineering and Computing Aims and scope Submit manuscript

Abstract

We propose a novel interpretation and usage of Neural Network (NN) in modeling physiological signals, which are allowed to be nonlinear and/or nonstationary. The method consists of training a NN for the k-step prediction of a physiological signal, and then examining the connection-weight-space (CWS) of the NN to extract information about the signal generator mechanism. We define a novel feature, Normalized Vector Separation (γ ij ), to measure the separation of two arbitrary states “i” and “j” in the CWS and use it to track the state changes of the generating system. The performance of the method is examined via synthetic signals and clinical EEG. Synthetic data indicates that γ ij can track the system down to a SNR of 3.5 dB. Clinical data obtained from three patients undergoing carotid endarterectomy of the brain showed that EEG could be modeled (within a root-means-squared-error of 0.01) by the proposed method, and the blood perfusion state of the brain could be monitored via γ ij , with small NNs having no more than 21 connection weight altogether.

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

Similar content being viewed by others

References

  1. Cisse Y, KinouchiY, Nagashino H, Akutagawa M (2002) BP neural networks approach for identifying biological signal source in circadian data fluctuations. IEICE Trans Inf Syst E85-D(3):568–576

    Google Scholar 

  2. Elbert T, Ray WJ, Kowalik ZJ, Skinner JE, Graf KE, Birbaumer N (1994) Chaos and physiology: deterministic chaos in excitable cell assemblies. Physiol Rev 74:1–47

    PubMed  Google Scholar 

  3. Funahashi K (1989) On the approximate realization of continuous mappings by neural networks. Neural Netw 2:183–192

    Article  Google Scholar 

  4. Gorman RP, Sejnowski TJ (1988) Analysis of hidden units in a layered network trained to classify sonar targets. Neural Netw 1:75–89

    Article  Google Scholar 

  5. Hinton GE (1992) How neural networks learn from experience. Sci Am 267:105–109

    Article  Google Scholar 

  6. Hornik K, Stinchombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2:359–366

    Article  Google Scholar 

  7. Japer H (1958) Ten-twenty electrode system of the international federation. Electroencephalogr Clin Neurophysiol 10:371–375

    Google Scholar 

  8. Jenkins GM, Watts DG (1969) Spectral analysis and its applications, Holden-Day series in time series analysis. Holden-Day, London

    Google Scholar 

  9. Kay SM (1988) Modern spectral estimation: theory and application. Prentice-Hall, NJ

    MATH  Google Scholar 

  10. Kirby SD, Eng P, Danter W, George CF, Francovic T, Ruby RR, Ferguson KA (1999) Neural network prediction of obstructive sleep apnea from clinical criteria. Chest 116:409–415

    Article  PubMed  Google Scholar 

  11. Li YC, Liu L, Chiu WT, Jian WS (2000) Neural network modeling for surgical decisions on traumatic brain injury patients. Med Infor 57:1–9

    Article  Google Scholar 

  12. Mackey C, Glass L (1977) Oscillation and chaos in physiological control systems. Science 197:287–289

    Article  PubMed  Google Scholar 

  13. Manuca R, Casdagli MC, Savit RS (1998) Nonstationarity in epileptic EEG and implications for neural dynamics. Math Biosci 147(1):1–22

    Article  PubMed  MATH  Google Scholar 

  14. Murray JD (1993) Mathematical biology, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  15. Oppenheim AV, Schafer RW (1989) Discrete-time signal processing. Prentice-Hall, Englewood Cliffs, NJ

    MATH  Google Scholar 

  16. Oud M (2002) Internal-state analysis in a layered artificial neural network trained to categorize lung sounds, man and cybernetics, Part A. IEEE Trans Syst 32:757–760

    Google Scholar 

  17. Packard NJ, Crutchfield JP, Farmer JD, Shaw RS (1980) Geometry from a time series. Phys Rev Lett 45:712–716

    Article  Google Scholar 

  18. Rieke C, Mormann F, Andrzejak RG, Kreuz T, David P, Elger CE, Lehnertz K (2003) Discerning nonstationarity from nonlinearity in seizure-free and preseizure EEG recordings from epilepsy patients. IEEE Trans Biomed Eng 50:634–639

    Article  PubMed  Google Scholar 

  19. Rumelhart DE, Hinton GE, Williams RJ (1986) Learning internal representation by error propagation. In: Rumelhart DE, McClelland JL, the PDP Research Group (eds) Parallel distributed processing. MIT press, Cambridge, pp 318–362

    Google Scholar 

  20. Takens F (1981) Detecting strange attractors in turbulence. In: Rand DA, Young LS (eds) Lecture notes in math, vol 898. Springer-Verlag, Berlin

  21. Varady P, Micsik T, Benedek S, Benyo Z (2002) A novel method for the detection of apnea and hypopnea events in respiration signals. IEEE Trans Biomed Eng 49:936–942

    Article  PubMed  Google Scholar 

  22. Watanabe E, Nakasako N, Mitani Y (1997) A prediction method of non-stationary time series data by using a modular structured neural network. IEICE Trans Fundamentals E80-A(6):971–976

    Google Scholar 

  23. Yu H, Bang S (1997) An improved time series prediction by applying the layer-by-layer learning method to FIR neural networks. Trans Soc Comput Simul Int 14:1717–1729

    Google Scholar 

Download references

Acknowledgments

This work was partly supported by Grants-in-Aid for Scientific Research #16560353 and #16700440 from Japan Society of Promotion of Science. The authors would like to thank The University of Queensland, Australia for access to facilities and hosting the first author as a Research Scholar during the work. Authors also thank Dr Fumio Shichijo (Department of Neurology, Suzue hospital, Tokushima, Japan) for providing them with clinical data for the work of this project.

Author information

Authors and Affiliations

  1. Faculty of Engineering, The University of Tokushima, Tokushima, Japan

    T. Emoto, M. Akutagawa & Y. Kinouchi

  2. School of Information Technology and Electrical Engineering, The University of Queensland, Queensland, Australia

    U. R. Abeyratne

  3. School of Health Sciences, The University of Tokushima, Tokushima, Japan

    H. Nagashino

Authors
  1. T. Emoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Akutagawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. U. R. Abeyratne
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. Nagashino
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Y. Kinouchi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Emoto.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Emoto, T., Akutagawa, M., Abeyratne, U.R. et al. Tracking the states of a nonlinear and nonstationary system in the weight-space of artificial neural networks. Med Bio Eng Comput 44, 146–159 (2006). https://doi.org/10.1007/s11517-005-0019-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-005-0019-8

Keywords

Search

Navigation