Medical & Biological Engineering & Computing

, Volume 57, Issue 6, pp 1297–1311 | Cite as

Quantifying mode mixing and leakage in multivariate empirical mode decomposition and application in motor imagery–based brain-computer interface system

  • Yang ZhengEmail author
  • Guanghua Xu
Original Article


Improper selection of the number and the amplitude of noise channels in noise-assisted multivariate empirical mode decomposition (NA-MEMD) would induce mode mixing and leakage in the obtained intrinsic mode functions (IMF), which would degrade the performance in applications like brain-computer interface (BCI) systems based on motor imagery. A measurement (ML-index) using no prior knowledge of the underlying components of the original signals was proposed to quantify the amount of mode mixing and leakage of IMFs. Both synthetic signals and electroencephalography (EEG) recordings from motor imagery experiments were used to test the validity. The BCI classification performance using NA-MEMD with the optimal parameters selected based on the ML-index was compared with the performance under the non-optimal parameter condition and the performance using the conventional filtering method. Test on synthetic signals demonstrated the ML-index can effectively quantify the amount of mode mixing and leakage, and help to improve the accuracy of extracting the underlying components. Test on EEG recordings showed the BCI classification performance can be significantly improved under the optimal parameter condition. This study provided a method to quantify the amount of mode mixing and leakage in IMFs and realized the optimization of the parameters associated with noise channels in NA-MEMD.

Graphical abstract

One of the synthetic multivariate signals comprised four components oscillating at different rates (middle column). Noise-assisted multivariate empirical mode decomposition (noise-assisted MEMD) was used to extract different components. Mode mixing issue occurred under the non-optimal parameter condition (left column). The issue was alleviated under the optimal parameter condition (right column) which can be obtained with the proposed method in this study.


Multivariate empirical mode decomposition Mode mixing BCI Motor imagery Intrinsic mode functions 


Funding information

This work was supported by the project funded by China Postdoctoral Science Foundation (Grant No. 2017M620445) and National Natural Science Foundation of China (Grant No. 51475360).

Compliance with ethical standards

Ethical approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Pfurtscheller G, Neuper C, Muller G, Obermaier B, Krausz G, Schlogl A, Scherer R, Graimann B, Keinrath C, Skliris D (2003) Graz-BCI: state of the art and clinical applications. IEEE Trans Neural Syst Rehabil Eng 11:1–4CrossRefGoogle Scholar
  2. 2.
    Vaughan TM, McFarland DJ, Schalk G, Sarnacki WA, Krusienski DJ, Sellers EW, Wolpaw JR (2006) The wadsworth BCI research and development program: at home with BCI. IEEE Trans Neural Syst Rehabil Eng 14:229–233CrossRefGoogle Scholar
  3. 3.
    Wolpaw JR, Birbaumer N, McFarland DJ, Pfurtscheller G, Vaughan TM (2002) Brain–computer interfaces for communication and control. Clin Neurophysiol 113:767–791CrossRefGoogle Scholar
  4. 4.
    Xu M, Xiao X, Wang Y, Qi H, Jung T-P, Ming D (2018) A brain–computer Interface based on miniature-event-related potentials induced by very small lateral visual stimuli. IEEE Trans Biomed Eng 65:1166–1175CrossRefGoogle Scholar
  5. 5.
    Xie J, Xu G, Wang J, Zhang S, Zhang F, Li Y, Han C, Li L (2014) Addition of visual noise boosts evoked potential-based brain-computer interface. Sci Rep 4:4953CrossRefGoogle Scholar
  6. 6.
    McCane LM, Heckman SM, McFarland DJ, Townsend G, Mak JN, Sellers EW, Zeitlin D, Tenteromano LM, Wolpaw JR, Vaughan TM (2015) P300-based brain-computer interface (BCI) event-related potentials (ERPs): people with amyotrophic lateral sclerosis (ALS) vs. age-matched controls. Clin Neurophysiol 126:2124–2131CrossRefGoogle Scholar
  7. 7.
    Hashimoto Y, Ushiba J (2013) EEG-based classification of imaginary left and right foot movements using beta rebound. Clin Neurophysiol 124:2153–2160CrossRefGoogle Scholar
  8. 8.
    Gao L, Wang J, Li J, Zheng Y Design of BCI based multi-information system to restore hand motor function for stroke patients. In: Systems, Man, and Cybernetics (SMC), 2013 IEEE International Conference on, 2013. IEEE, pp 4924–4928Google Scholar
  9. 9.
    Nam CS, Jeon Y, Kim Y-J, Lee I, Park K (2011) Movement imagery-related lateralization of event-related (de) synchronization (ERD/ERS): motor-imagery duration effects. Clin Neurophysiol 122:567–577CrossRefGoogle Scholar
  10. 10.
    Pfurtscheller G, Brunner C, Schlögl A, Da Silva FL (2006) Mu rhythm (de) synchronization and EEG single-trial classification of different motor imagery tasks. Neuroimage 31:153–159CrossRefGoogle Scholar
  11. 11.
    Alonso-Valerdi LM, Salido-Ruiz RA, Ramirez-Mendoza RA (2015) Motor imagery based brain–computer interfaces: an emerging technology to rehabilitate motor deficits. Neuropsychologia 79:354–363CrossRefGoogle Scholar
  12. 12.
    Ang KK, Chua KSG, Phua KS, Wang C, Chin ZY, Kuah CWK, Low W, Guan C (2015) A randomized controlled trial of EEG-based motor imagery brain-computer interface robotic rehabilitation for stroke. Clin EEG Neurosci 46:310–320CrossRefGoogle Scholar
  13. 13.
    Ge S, Wang R, Yu D (2014) Classification of four-class motor imagery employing single-channel electroencephalography. PLoS One 9:e98019CrossRefGoogle Scholar
  14. 14.
    Liu Y, Li M, Zhang H, Wang H, Li J, Jia J, Wu Y, Zhang L (2014) A tensor-based scheme for stroke patients’ motor imagery EEG analysis in BCI-FES rehabilitation training. J Neurosci Methods 222:238–249CrossRefGoogle Scholar
  15. 15.
    Park C, Looney D, Kidmose P, Ungstrup M, Mandic DP (2011) Time-frequency analysis of EEG asymmetry using bivariate empirical mode decomposition. IEEE Trans Neural Syst Rehabil Eng 19:366–373CrossRefGoogle Scholar
  16. 16.
    Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen N-C, Tung CC, Liu HH (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. In: Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences, . The Royal Society, pp 903–995, 454Google Scholar
  17. 17.
    Bajaj V, Pachori RB (2012) Classification of seizure and nonseizure EEG signals using empirical mode decomposition. IEEE Trans Inf Technol Biomed 16:1135–1142CrossRefGoogle Scholar
  18. 18.
    Huang L, Huang X, Wang Y-T, Wang Y, Jung T-P, Cheng C-K (2013).Empirical mode decomposition improves detection of SSVEP. In: Engineering in Medicine and Biology Society (EMBC), 2013 35th Annual International Conference of the IEEE, IEEE, pp 3901–3904Google Scholar
  19. 19.
    Zeng H, Song A, Yan R, Qin H (2013) EOG artifact correction from EEG recording using stationary subspace analysis and empirical mode decomposition. Sensors 13:14839–14859CrossRefGoogle Scholar
  20. 20.
    Looney D, Park C, Kidmose P, Ungstrup M, Mandic D (2009) Measuring phase synchrony using complex extensions of EMD. In: Statistical Signal Processing, SSP'09. IEEE/SP 15th Workshop on, 2009. IEEE, pp 49–52Google Scholar
  21. 21.
    Zheng Y, Wang G, Wang J (2016) Is using threshold-crossing method and single type of features sufficient to achieve realistic application of seizure prediction? Clin EEG Neurosci 47:305–316CrossRefGoogle Scholar
  22. 22.
    Zheng Y, Wang G, Li K, Bao G, Wang J (2014) Epileptic seizure prediction using phase synchronization based on bivariate empirical mode decomposition. Clin Neurophysiol 125:1104–1111CrossRefGoogle Scholar
  23. 23.
    Rilling G, Flandrin P, Fellow, Gonçalves P, Lilly JM (2007) Bivariate empirical mode decomposition. IEEE SIGNAL PROCESSING LETTERS:10Google Scholar
  24. 24.
    ur Rehman N, Mandic DP (2010) Empirical mode decomposition for trivariate signals. IEEE Trans Signal Process 58:1059–1068CrossRefGoogle Scholar
  25. 25.
    Rehman N, Mandic DP Multivariate empirical mode decomposition.(2009) In: Proceedings of The Royal Society of London A: Mathematical, Physical and Engineering Sciences The Royal Society, p rspa20090502Google Scholar
  26. 26.
    Huang NE, Shen Z, Long SR (1999) A new view of nonlinear water waves: the Hilbert spectrum. Annu Rev Fluid Mech 31:417–457CrossRefGoogle Scholar
  27. 27.
    Wu Z, Huang NE (2009) Ensemble empirical mode decomposition: a noise-assisted data analysis method. Adv Adapt Data Anal 1:1–41CrossRefGoogle Scholar
  28. 28.
    Flandrin P, Rilling G, Goncalves P (2004) Empirical mode decomposition as a filter bank. IEEE Signal Process Lett 11:112–114CrossRefGoogle Scholar
  29. 29.
    Wu Z, Huang NE (2004) A study of the characteristics of white noise using the empirical mode decomposition method. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences,. vol 2046. The Royal Society, pp 1597–1611, 460Google Scholar
  30. 30.
    Ur Rehman N, Mandic DP (2011) Filter bank property of multivariate empirical mode decomposition. IEEE Trans Signal Process 59:2421–2426CrossRefGoogle Scholar
  31. 31.
    Boord P, Craig A, Tran Y, Nguyen H (2010) Discrimination of left and right leg motor imagery for brain–computer interfaces. Med Biol Eng Comput 48:343–350CrossRefGoogle Scholar
  32. 32.
    Hjorth B (1975) An on-line transformation of EEG scalp potentials into orthogonal source derivations. Electroencephalogr Clin Neurophysiol 39:526–530CrossRefGoogle Scholar
  33. 33.
    Müller-Gerking J, Pfurtscheller G, Flyvbjerg H (1999) Designing optimal spatial filters for single-trial EEG classification in a movement task. Clin Neurophysiol 110:787–798CrossRefGoogle Scholar
  34. 34.
    Atyabi A, Shic F, Naples A (2016) Mixture of autoregressive modeling orders and its implication on single trial EEG classification. Expert Syst Appl 65:164–180CrossRefGoogle Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2019

Authors and Affiliations

  1. 1.State Key Laboratory for Manufacturing Systems Engineering, School of Mechanical EngineeringXi’an Jiaotong UniversityXi’anChina

Personalised recommendations