Skip to main content
SpringerLink
Log in

On the robustness of EEG tensor completion methods

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

During the acquisition of electroencephalographic (EEG) signals, data may be missing or corrupted by noise and artifacts. To reconstruct the incomplete data, EEG signals are firstly converted into a three-order tensor (multi-dimensional data) of shape time × channel × trial. Then, the missing data can be efficiently recovered by applying a tensor completion method (TCM). However, there is not a unique way to organize channels and trials in a tensor, and different numbers of channels are available depending on the EEG setting used, which may affect the quality of the tensor completion results. The main goal of this paper is to evaluate the robustness of EEG completion methods with several designed parameters such as the ordering of channels and trials, the number of channels, and the amount of missing data. In this work, the results of completing missing data by several TCMs were compared. To emulate different scenarios of missing data, three different patterns of missing data were designed. Firstly, the amount of missing data on completion effects was analyzed, including the time lengths of missing data and the number of channels or trials affected by missing data. Secondly, the numerical stability of the completion methods was analyzed by shuffling the indices along channels or trials in the EEG data tensor. Finally, the way that the number of electrodes of EEG tensors influences completion effects was assessed by changing the number of channels. Among all the applied TCMs, the simultaneous tensor decomposition and completion (STDC) method achieves the best performance in providing stable results when the amount of missing data or the electrode number of EEG tensors is changed. In other words, STDC proves to be an excellent choice of TCM, since permutations of trials or channels have almost no influence on the complete results. The STDC method can efficiently complete the missing EEG signals. The designed simulations can be regarded as a procedure to validate whether or not a completion method is useful enough to complete EEG signals.

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. Lotte F, Congedo M, Lécuyer A, et al. A review of classification algorithms for EEG-based brain computer interfaces. J Neur Eng, 2007, 4: 1–13

    Article  Google Scholar 

  2. Sakhavi S. Application of deep learning methods in brain-computer interface systems. Dissertation for Doctoral Degree. Singapore: National University of Singapore, 2017

    Google Scholar 

  3. Lin Z, Zhang C, Wu W, et al. Frequency recognition based on canonical correlation analysis for SSVEP-based BCIs. IEEE Trans Biomed Eng, 2006, 53: 2610–2614

    Article  Google Scholar 

  4. Donchin E, Spencer K M, Wijesinghe R. The mental prosthesis: Assessing the speed of a P300-based brain-computer interface. IEEE Trans Rehab Eng, 2000, 8: 174–179

    Article  Google Scholar 

  5. Pfurtscheller G, Neuper C. Motor imagery and direct brain-computer communication. Proc IEEE, 2001, 89: 1123–1134

    Article  Google Scholar 

  6. Jin J, Li S, Daly I, et al. The study of generic model set for reducing calibration time in P300-based brain-computer interface. IEEE Trans Neur Syst Rehabil Eng, 2020, 28: 3–12

    Article  Google Scholar 

  7. Solé-Casals J, Caiafa C F, Zhao Q, et al. Brain-computer interface with corrupted EEG data: A tensor completion approach. Cogn Comput, 2018, 10: 1062–1074

    Article  Google Scholar 

  8. Neuper C, Wrtz M, Pfurtscheller G. ERD/ERS patterns reflecting sensorimotor activation and deactivation. Progress Brain Res, 2006, 159: 211–222

    Article  Google Scholar 

  9. Jin J, Allison B Z, Zhang Y, et al. An ERP-based BCI using an oddball paradigm with different faces and reduced errors in critical functions. Int J Neur Syst, 2014, 24: 1450027

    Article  Google Scholar 

  10. Lisi G, Rivela D, Takai A, et al. Markov switching model for quick detection of event related desynchronization in EEG. Front Neurosci, 2018, 12: 24

    Article  Google Scholar 

  11. Zhang L, Song L, Du B, et al. Nonlocal low-rank tensor completion for visual data. IEEE Trans Cybern, 2021, 51: 673–685

    Article  Google Scholar 

  12. Gunnarsdottir K M, Bulacio J, Gonzalez-Martinez J, et al. Estimating intracranial EEG signals at missing electrodes in epileptic networks. In: Proceedings of the 41st Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC). Berlin, 2019

  13. Cichocki A, Lee N, Oseledets I, et al. Tensor networks for dimensionality reduction and large-scale optimization: Part 1 low-rank tensor decompositions. FNT Mach Learn, 2016, 9: 249–429

    Article  Google Scholar 

  14. Zhou G, Zhao Q, Zhang Y, et al. Linked component analysis from matrices to high-order tensors: Applications to biomedical data. Proc IEEE, 2016, 104: 310–331

    Article  Google Scholar 

  15. Shi Q, Cheung Y M, Zhao Q, et al. Feature extraction for incomplete data via low-rank tensor decomposition with feature regularization. IEEE Trans Neur Netw Learn Syst, 2019, 30: 1803–1817

    Article  MathSciNet  Google Scholar 

  16. Yu J, Li C, Zhao Q, et al. Tensor-ring nuclear norm minimization and application for visual: Data completion. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Brighton, 2019. 3142–3146

  17. Sorensen M, de Lathauwer L. Fiber sampling approach to canonical polyadic decomposition and application to tensor completion. SIAM J Matrix Anal Appl, 2019, 40: 888–917

    Article  MathSciNet  Google Scholar 

  18. Gu Y, Liu T, Li J. Superpixel tensor model for spatial-spectral classification of remote sensing images. IEEE Trans Geosci Remote Sens, 2019, 57: 4705–4719

    Article  Google Scholar 

  19. Cui G, Gui L, Zhao Q, et al. Bayesian CP factorization of incomplete tensor for EEG signal application. In: Proceedings of the IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). Vancouver, 2016. 2170–2173

  20. Ofner P, Schwarz A, Pereira J, et al. Upper limb movements can be decoded from the time-domainoflow-frequency EEG. PLoS ONE, 2017, 12: 0182578

    Article  Google Scholar 

  21. Acar E, Dunlavy D M, Kolda T G, et al. Scalable tensor factorizations for incomplete data. Chemometr Intell Lab Syst, 2011, 106: 41–56

    Article  Google Scholar 

  22. Cichocki A, Mandic D, de Lathauwer L, et al. Tensor decompositions for signal processing applications: From two-way to multiway component analysis. IEEE Signal Process Mag, 2015, 32: 145–163

    Article  Google Scholar 

  23. Zhao Q, Zhang L, Cichocki A. Bayesian CP factorization of incomplete tensors with automatic rank determination. IEEE Trans Pattern Anal Mach Intell, 2015, 37: 1751–1763

    Article  Google Scholar 

  24. Chen Y L, Hsu C T, Liao H Y M. Simultaneous tensor decomposition and completion using factor priors. IEEE Trans Pattern Anal Mach Intell, 2014, 36: 577–591

    Article  Google Scholar 

  25. Liu J, Musialski P, Wonka P, et al. Tensor completion for estimating missing values in visual data. IEEE Trans Pattern Anal Mach Intell, 2013, 35: 208–220

    Article  Google Scholar 

  26. Nakanishi M, Wang Y, Chen X, et al. Enhancing detection of SSVEPs for a high-speed brain speller using task-related component analysis. IEEE Trans Biomed Eng, 2018, 65: 104–112

    Article  Google Scholar 

  27. Xie Q, Zhao Q, Meng D, et al. Kronecker-basis-representation based tensor sparsity and its applications to tensor recovery. IEEE Trans Pattern Anal Mach Intell, 2018, 40: 1888–1902

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Artificial Intelligence, Nankai University, Tianjin, 300350, China

    Feng Duan, Hao Jia, ZhiWen Zhang, Fan Feng, Ying Tan, YangYang Dai, Cesar F. Caiafa, Zhe Sun & Jordi Solé-Casals

  2. Skolkowo Institute of Science and Technology, Moscow, 121205, Russia

    Andrzej Cichocki

  3. College of Computer Science, Hangzhou Dianzi University, Hangzhou, 310018, China

    Andrzej Cichocki

  4. Department of Informatics, Nicolaus Copernicus University, Torun, 87-100, Poland

    Andrzej Cichocki

  5. Systems Research Institute, Polish Academy of Sciences, Warsaw, 01-447, Poland

    Andrzej Cichocki

  6. College of Computer Science, Nankai University, Tianjin, 300350, China

    ZhengLu Yang

  7. Instituto Argentino de Radioastronomía IAR-CCT La Plata, CONICET/CIC-PBA/UNLP, Villa Elisa, 1894, Argentina

    Cesar F. Caiafa

  8. Computational Engineering Applications Unit, Head Office for Information Systems and Cybersecurity, RIKEN, Wako-Shi, 351-0106, Japan

    Zhe Sun

  9. Department of Psychiatry, University of Cambridge, Cambridge, CB2 8AH, UK

    Jordi Solé-Casals

  10. Data and Signal Processing Research Group, University of Vic-Central University of Catalonia, Catalonia, 08500, Spain

    Jordi Solé-Casals

Authors
  1. Feng Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hao Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. ZhiWen Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fan Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ying Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. YangYang Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Andrzej Cichocki
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. ZhengLu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Cesar F. Caiafa
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Zhe Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Jordi Solé-Casals
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Feng Duan, Cesar F. Caiafa, Zhe Sun or Jordi Solé-Casals.

Additional information

This work was supported by the National Key R&D Program of China (Grant No. 2017YFE0129700), the National Natural Science Foundation of China (Key Program) (Grant No. 11932013), the National Natural Science Foundation of China (Grant No. 61673224), the Tianjin Natural Science Foundation for Distinguished Young Scholars (Grant No. 18JCJQJC46100), the Tianjin Science and Technology Plan Project (Grant No. 18ZXJMTG00260), and in part by the Ministry of Education and Science of the Russian Federation (Grant No. 14.756.31.0001). SOLÉ-CASALS Jordi work was supported by COST (European Cooperation in Science and Technology) Action (Grant No. CA18106). CAIAFA Cesar F. Work was supported by Proyectos de Investigación Científica y Tecnológica (PICT) (Grant No. 2017-3208) and Proyectos Universidad de Buenos Aires Ciencia y Técnica (UBACyT) (Grant No. 20020170100192BA).

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Duan, F., Jia, H., Zhang, Z. et al. On the robustness of EEG tensor completion methods. Sci. China Technol. Sci. 64, 1828–1842 (2021). https://doi.org/10.1007/s11431-020-1839-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-020-1839-5

Keywords

Search

Navigation