, Volume 17, Issue 2, pp 235–251 | Cite as

Characterizing Regularization Techniques for Spatial Filter Optimization in Oscillatory EEG Regression Problems

Guidelines Derived from Simulation and Real-World Data
  • Andreas MeinelEmail author
  • Sebastián Castaño-Candamil
  • Benjamin Blankertz
  • Fabien Lotte
  • Michael TangermannEmail author
Original Article


We report on novel supervised algorithms for single-trial brain state decoding. Their reliability and robustness are essential to efficiently perform neurotechnological applications in closed-loop. When brain activity is assessed by multichannel recordings, spatial filters computed by the source power comodulation (SPoC) algorithm allow identifying oscillatory subspaces. They regress to a known continuous trial-wise variable reflecting, e.g. stimulus characteristics, cognitive processing or behavior. In small dataset scenarios, this supervised method tends to overfit to its training data as the involved recordings via electroencephalogram (EEG), magnetoencephalogram or local field potentials generally provide a low signal-to-noise ratio. To improve upon this, we propose and characterize three types of regularization techniques for SPoC: approaches using Tikhonov regularization (which requires model selection via cross-validation), combinations of Tikhonov regularization and covariance matrix normalization as well as strategies exploiting analytical covariance matrix shrinkage. All proposed techniques were evaluated both in a novel simulation framework and on real-world data. Based on the simulation findings, we saw our expectations fulfilled, that SPoC regularization generally reveals the largest benefit for small training sets and under severe label noise conditions. Relevant for practitioners, we derived operating ranges of regularization hyperparameters for cross-validation based approaches and offer open source code. Evaluating all methods additionally on real-world data, we observed an improved regression performance mainly for datasets from subjects with initially poor performance. With this proof-of-concept paper, we provided a generalizable regularization framework for SPoC which may serve as a starting point for implementing advanced techniques in the future.


EEG bandpower Subspace decomposition Brain-computer interface Single trial analysis Source power comodulation Brain state decoding algorithm 



This work was fully supported by BrainLinks-BrainTools Cluster of Excellence funded by the German Research Foundation (DFG), grant number EXC1086. For the data analysis, the authors acknowledge support by the state of Baden-Württemberg through bwHPC and the German Research Foundation (DFG) by grant no. INST 39/963-1 FUGG. Fabien Lotte received research support from the French National Research Agency with the REBEL project (grant ANR-15-CE23-0013-01) and the European Research Council with the BrainConquest project (grant ERC-2016-STG-714567). For parts of the data analysis, the Matlab-based BBCI toolbox was utilized (Blankertz et al. 2016). The authors declare that they have no conflict of interest.


  1. Arvaneh, M., Guan, C., Ang, K.K., Quek, C. (2011). Optimizing the channel selection and classification accuracy in EEG-based BCI. IEEE Transactions on Biomedical Engineering, 58(6), 1865–1873. Scholar
  2. Arvaneh, M., Guan, C., Ang, K.K., Quek, C. (2013). Optimizing spatial filters by minimizing within-class dissimilarities in electroencephalogram-based brain-computer interface. IEEE Transactions on Neural Networks and Learning Systems, 24(4), 610–619. Scholar
  3. Bai, Z, & Silverstein, JW. (2009). Spectral analysis of large dimensional random matrices. Springer Science & Business Media.Google Scholar
  4. Bartz, D., & Müller, K.-R. (2014). Covariance shrinkage for autocorrelated data. In Ghahramani, Z., Welling, M., Cortes, C., Lawrence, N.D., Weinberger, K.Q. (Eds.) Advances in neural information processing systems, (Vol. 27 pp. 1592–1600): Curran Associates Inc.Google Scholar
  5. Blankertz, B., Tomioka, R., Lemm, S., Kawanabe, M., Müller, K.-R. (2008). Optimizing spatial filters for robust EEG single-trial analysis. Signal Processing Magazine, IEEE, 25(1), 41–56.CrossRefGoogle Scholar
  6. Blankertz, B., Sannelli, C., Halder, S., Hammer, E.M., Kübler, A., Müller, K.-R., Curio, G., Dickhaus, T. (2010). Neurophysiological predictor of SMR-based BCI performance. NeuroImage, 51(4), 1303–1309. Scholar
  7. Blankertz, B., Acqualagna, L., Dähne, S, Haufe, S., Schultze-Kraft, M., Sturm, I., Ušćumlic, M., Wenzel, M.A., Curio, G., Müller, K.-R. (2016). The berlin brain-computer interface: progress beyond communication and control. Frontiers in Neuroscience, 10, 530. Scholar
  8. Castaño-Candamil, J.S., Meinel, A., Dähne, S., Tangermann, M. (2015). Probing meaningfulness of oscillatory EEG components with bootstrapping, label noise and reduced training sets. In 2015 37th Annual international conference of the IEEE engineering in medicine and biology society (EMBC) (pp. 5159–5162). IEEE.Google Scholar
  9. Castaño-Candamil, S., Meinel, A., Tangermann, M. (2017). Post-hoc labeling of arbitrary EEG recordings for data-efficient evaluation of neural decoding methods. arXiv:171108208.
  10. Chen, Y., Wiesel, A., Hero, A.O. (2011). Robust shrinkage estimation of high-dimensional covariance matrices. IEEE Transactions on Signal Processing, 59(9), 4097–4107. Scholar
  11. Cheng, M., Lu, Z., Wang, H. (2017). Regularized common spatial patterns with subject-to-subject transfer of EEG signals. Cognitive Neurodynamics, 11(2), 173–181. Scholar
  12. Cho, H., Ahn, M., Kim, K., Jun, S.C. (2015). Increasing session-to-session transfer in a brain–computer interface with on-site background noise acquisition. Journal of Neural Engineering, 12(6), 066,009. Scholar
  13. Clerc, M., Bougrain, L., Lotte, F. (2016). Brain-computer interfaces 2: technology and applications. Wiley.Google Scholar
  14. Dähne, S., Meinecke, F.C., Haufe, S., Höhne, J, Tangermann, M., Müller, K.-R., Nikulin, V.V. (2014). SPoC: a novel framework for relating the amplitude of neuronal oscillations to behaviorally relevant parameters. NeuroImage, 86(0), 111–122. Scholar
  15. de Cheveigné, A., & Parra, L.C. (2014). Joint decorrelation, a versatile tool for multichannel data analysis. NeuroImage, 98(Supplement C), 487–505. Scholar
  16. De Bie, T., Cristianini, N., Rosipal, R. (2005). Eigenproblems in pattern recognition. In Handbook of geometric computing (pp. 129–167). Springer.Google Scholar
  17. De Vos, M., Riès, S., Vanderperren, K., Vanrumste, B., Alario, F.X., Huffel, V.S., Burle, B. (2010). Removal of muscle artifacts from EEG recordings of spoken language production. Neuroinformatics, 8(2), 135–150. Scholar
  18. Devlaminck, D., Wyns, B., Grosse-Wentrup, M., Otte, G., Santens, P. (2011). Multisubject learning for common spatial patterns in motor-imagery BCI. Intelligence Neuroscience, 2011, 8:8–8:8. Scholar
  19. Engemann, D.A., & Gramfort, A. (2015). Automated model selection in covariance estimation and spatial whitening of MEG and EEG signals. NeuroImage, 108, 328–342. Scholar
  20. Farina, D., Jiang, N., Rehbaum, H., Holobar, A., Graimann, B., Dietl, H., Aszmann, O.C. (2014). The extraction of neural information from the surface EMG for the control of upper-limb prostheses: emerging avenues and challenges. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 22(4), 797–809. Scholar
  21. Farquhar, J., & Hill, N.J. (2013). Interactions between pre-processing and classification methods for event-related-potential classification. Neuroinformatics, 11(2), 175–192. Scholar
  22. Farquhar, J., Hill, N., Lal, T.N., Schölkopf, B. (2006). Regularised CSP for sensor selection in BCI. In Proceedings of the 3rd international BCI workshop.Google Scholar
  23. Fawcett, T. (2006). An introduction to ROC analysis. Pattern Recognition Letters, 27(8), 861–874.CrossRefGoogle Scholar
  24. Frey, J., Daniel, M., Hachet, M., Castet. J., Lotte, F. (2016). Framework for electroencephalography-based evaluation of user experience. InProcedings of CHI (pp. 2283–2294).Google Scholar
  25. Grosse-Wentrup, M., Liefhold, C., Gramann, K., Buss, M. (2009). Beamforming in non invasive brain-computer interfaces. IEEE Transactions on Biomedical Engineering, 56(4), 1209–1219.CrossRefGoogle Scholar
  26. Hyvarinen, A. (1999). Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks, 10(3), 626–634. Scholar
  27. Kang, H., Nam, Y., Choi, S. (2009). Composite common spatial pattern for subject-to-subject transfer. IEEE Signal Processing Letters, 16(8), 683–686. Scholar
  28. Kenney, J.F. (2013). Mathematics of statistics. Toronto: D. Van Nostrand Company Inc. Princeton; New Jersey; London; New York,; Affiliated East-West Press Pvt-Ltd; New Delhi.Google Scholar
  29. Koles, Z.J. (1991). The quantitative extraction and topographic mapping of the abnormal components in the clinical EEG. Electroencephalography and clinical Neurophysiology, 79(6), 440–447.CrossRefGoogle Scholar
  30. Krusienski, D., Grosse-Wentrup, M., Galán, F., Coyle, D., Miller, K., Forney, E., Anderson, C. (2011). Critical issues in state-of-the-art brain-computer interface signal processing. Journal of Neural Engineering, 8(2), 025,002.CrossRefGoogle Scholar
  31. Ledoit, O., & Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2), 365–411. Scholar
  32. Lotte, F. (2015). Signal processing approaches to minimize or suppress calibration time in oscillatory activity-based brain-computer interfaces. Proceedings of the IEEE, 103(6), 871–890. Scholar
  33. Lotte, F., & Guan, C. (2010). Learning from other subjects helps reducing brain-computer interface calibration time. In 2010 IEEE International conference on acoustics, speech and signal processing (pp. 614–617).
  34. Lotte, F., & Guan, C. (2011). Regularizing common spatial patterns to improve BCI designs: unified theory and new algorithms. IEEE Transactions on Biomedical Engineering, 58(2), 355–362. Scholar
  35. Lu, H., Eng, H.L., Guan, C., Plataniotis, K.N., Venetsanopoulos, A.N. (2010). Regularized common spatial pattern with aggregation for EEG classification in small-sample setting. IEEE Transactions on Biomedical Engineering, 57(12), 2936–2946. Scholar
  36. Mahmud, M., Kaiser, M.S., Hussain, A., Vassanelli, S. (2018). Applications of deep learning and reinforcement learning to biological data. IEEE Transactions on Neural Networks and Learning Systems, 29(6), 2063–2079. Scholar
  37. Makeig, S., Debener, S., Onton, J., Delorme, A. (2004). Mining event-related brain dynamics. Trends in Cognitive Sciences, 8(5), 204–210. Scholar
  38. Makeig, S., Kothe, C., Mullen, T., Bigdely-Shamlo, N., Zhang, Z., Kreutz-Delgado, K. (2012). Evolving signal processing for brain-computer interfaces. Proceedings of the IEEE, 100(Special Centennial Issue), 1567–1584. Scholar
  39. Mattout, J., Phillips, C., Penny, W.D., Rugg, M.D., Friston, K.J. (2006). MEG source localization under multiple constraints: an extended Bayesian framework. NeuroImage, 30(3), 753–767. Scholar
  40. Meinel, A., Castaño-Candamil, S, Reis, J., Tangermann, M. (2016). Pre-trial EEG-based single-trial motor performance prediction to enhance neuroergonomics for a hand force task. Frontiers in Human Neuroscience, 10, 170. Scholar
  41. Meinel, A., Lotte, F., Tangermann, M. (2017). Tikhonov regularization enhances EEG-based spatial filtering for single-trial regression. In Proceedings of the 7th Graz brain-computer interface conference 2017 (pp. 308-313).
  42. Millán, J.d.R., Rupp, R., Mueller-Putz, G., Murray-Smith, R., Giugliemma, C., Tangermann, M., Vidaurre, C., Cincotti, F., Kübler, A, Leeb, R., Neuper, C., Müller, K.-R, Mattia, D. (2010). Combining brain–computer interfaces and assistive technologies: state-of-the-art and challenges. Frontiers in Neuroscience, 4, 161.Google Scholar
  43. Nicolae, I.E., Acqualagna, L., Blankertz, B. (2017). Assessing the depth of cognitive processing as the basis for potential user-state adaptation. Frontiers in Neuroscience, 11.
  44. Park, S.H., Lee, D., Lee, S.G. (2017). Filter bank regularized common spatial pattern ensemble for small sample motor imagery classification. IEEE Transactions on Neural Systems and Rehabilitation Engineering, PP(99), 1–1. Scholar
  45. Parra, L.C., Spence, C.D., Gerson, A.D., Sajda, P. (2005). Recipes for the linear analysis of EEG. NeuroImage, 28(2), 326–341.CrossRefGoogle Scholar
  46. Ramanathan, C., Ghanem, R.N., Jia, P., Ryu, K., Rudy, Y. (2004). Noninvasive electrocardiographic imaging for cardiac electrophysiology and arrhythmia. Nature Medicine, 10(4), nm1011. Scholar
  47. Ramoser, H., Muller-Gerking, J., Pfurtscheller, G. (2000). Optimal spatial filtering of single trial EEG during imagined hand movement. IEEE Transactions on Rehabilitation Engineering, 8(4), 441–446.CrossRefGoogle Scholar
  48. Reuderink, B., & Poel, M. (2008). Robustness of the common spatial patterns algorithm in the BCI-pipeline. Tech rep. HMI, University of Twente.Google Scholar
  49. Samek, W., Vidaurre, C., Müller, K.-R., Kawanabe, M. (2012). Stationary common spatial patterns for brain-computer interfacing. Journal of Neural Engineering, 9(2), 026,013. Scholar
  50. Samek, W., Meinecke, F.C., Müller, K.-R. (2013). Transferring subspaces between subjects in brain-computer interfacing. IEEE Transactions on Biomedical Engineering, 60(8), 2289–2298. Scholar
  51. Samek, W., Kawanabe, M., Müller, K.-R. (2014). Divergence-based framework for common spatial patterns algorithms. IEEE Reviews in Biomedical Engineering, 7, 50–72. Scholar
  52. Schäfer, J., & Strimmer, K. (2005). A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology, 4, 1.CrossRefGoogle Scholar
  53. Schultze-Kraft, M., Dähne, S, Gugler, M., Curio, G., Blankertz, B. (2016). Unsupervised classification of operator workload from brain signals. Journal of Neural Engineering, 13(3), 036,008. Scholar
  54. Tian, T.S., Huang, J.Z., Shen, H., Li, Z. (2013). EEG/MEG source reconstruction with spatial-temporal two-way regularized regression. Neuroinformatics, 11(4), 477–493. Scholar
  55. Tikhonov, A.N. (1963). Regularization of incorrectly posed problems. Soviet Mathematics Doklady, 4, 1624–1627.Google Scholar
  56. Úbeda, A., Azorín, J.M., Chavarriaga, R., Millán, J.d.R. (2017). Classification of upper limb center-out reaching tasks by means of EEG-based continuous decoding techniques. Journal of NeuroEngineering and Rehabilitation, 14, 9. Scholar
  57. Wang, H., & Li, X. (2016). Regularized filters for L1-norm-based common spatial patterns. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 24(2), 201–211. Scholar
  58. Winkler, I., Brandl, S., Horn, F., Waldburger, E., Allefeld, C., Tangermann, M. (2014). Robust artifactual independent component classification for bci practitioners. Journal of Neural Engineering, 11(3), 035,013.CrossRefGoogle Scholar
  59. Wu, D., King, J.T., Chuang, C.H., Lin, C.T., Jung, T.P. (2017). Spatial filtering for EEG-based regression problems in brain-computer interface (BCI). IEEE Transactions on Fuzzy Systems, PP(99), 1–1. Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Brain State Decoding Lab, Cluster of Excellence BrainLinks-BrainTools, Department of Computer ScienceAlbert-Ludwigs-UniversityFreiburgGermany
  2. 2.Neurotechnology Dept.Technical University of BerlinBerlinGermany
  3. 3.Potioc project teamInriaTalenceFrance
  4. 4.LaBRI (University of Bordeaux, CNRS, INP)TalenceFrance

Personalised recommendations