A Theoretical Derivation of the Kernel Extreme Energy Ratio Method for EEG Feature Extraction

  • Shiliang Sun
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5326)


In the application of brain-computer interfaces (BCIs), energy features are both physiologically well-founded and empirically effective to describe electroencephalogram (EEG) signals for classifying brain activities. Recently, a linear method named extreme energy ratio (EER) for energy feature extraction of EEG signals in terms of spatial filtering was proposed. This paper gives a nonlinear extension of the linear EER method. Specifically, we use the kernel trick to derive a kernelized version of the original EER feature extractor. The solutions for optimizing the criterion in kernel EER are provided for future use.


brain-computer interface (BCI) extreme energy ratio (EER) EEG signal classification feature extraction kernel machine 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Nicolelis, M.A.L.: Actions from Thoughts. Nature 409, 403–407 (2001)CrossRefGoogle Scholar
  2. 2.
    Wolpaw, J.R., Birbaumer, N., McFarland, D.J., Pfurtscheller, G., Vaughan, T.M.: Brain-Computer Interfaces for Communication and Control. Clin. Neurophysiol. 113, 767–791 (2002)CrossRefGoogle Scholar
  3. 3.
    Sun, S.: The Extreme Energy Ratio Criterion for EEG Feature Extraction. In: Proc. 18th Int. Conf. Artificial Neural Networks, Prague, Czech Republic (2008)Google Scholar
  4. 4.
    Müller-Gerking, J., Pfurtscheller, G., Flyvbjerg, H.: Designing Optimal Spatial Filters for Single-Trial EEG Classification in a Movement Task. Clin. Neurophysiol. 110, 787–798 (1999)CrossRefGoogle Scholar
  5. 5.
    Müller, K.R., Mika, S., Rätsch, G., Tsuda, K., Schölkopf, B.: An Introduction to Kernel-Based Learning Algorithms. IEEE Trans. Neural Netw. 12, 181–201 (2001)CrossRefGoogle Scholar
  6. 6.
    Curran, E.A., Stokes, M.J.: Learning to Control Brain Activity: A Review of the Production and Control of EEG Components for Driving Brain-Computer Interface (BCI) Systems. Brain Cogn. 51, 326–336 (2003)CrossRefGoogle Scholar
  7. 7.
    Kamousi, B., Liu, Z., He, B.: Classification of Motor Imagery Tasks for Brain-Computer Interface Applications by Means of Two Equivalent Dipoles Analysis. IEEE Trans. Neural Syst. Rehabil. Eng. 13, 166–171 (2005)CrossRefGoogle Scholar
  8. 8.
    Aizerman, M., Braverman, E., Rozonoer, L.: Theoretical Foundations of the Potential Function Method in Pattern Recognition Learning. Automation and Remote Control 25, 821–837 (1964)zbMATHGoogle Scholar
  9. 9.
    Schölkopf, B., Smola, A., Müller, K.R.: Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Comput. 10, 1299–1319 (1998)CrossRefGoogle Scholar
  10. 10.
    Mika, S., Rätsch, G., Weston, J., Schölkopf, B., Müller, K.R.: Fisher Discriminant Analysis with Kernels. In: Proc. IEEE Int. Workshop Neural Networks for Signal Processing IX, Madison, USA, pp. 41–48 (1999)Google Scholar
  11. 11.
    Vapnik, V.: The Nature of Statistical Learning Theory, 2nd edn. Springer, New York (2000)CrossRefzbMATHGoogle Scholar
  12. 12.
    Schölkopf, B., Smola, A.: Learning with Kernels: Support Vector Machines, Regularization, Optimization and Beyond. MIT Press, Cambridge (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Shiliang Sun
    • 1
  1. 1.Department of Computer Science and TechnologyEast China Normal UniversityShanghaiChina

Personalised recommendations