Brain Topography

, Volume 12, Issue 4, pp 263–271 | Cite as

Trilinear Modeling of Event-Related Potentials

  • Kongming Wang
  • Henri Begleiter
  • Bernice Porjesz


This paper describes a method for estimating a set of spatial components (brain maps) and temporal components (waveforms) of brain potentials. These components play the role of bases of a coordinate system, in the sense that the brain potentials of any subject can be represented as superpositions of these components. The representation is unique given the spatial and temporal components, and this decomposition is particularly appealing for comparing the brain potentials of different subjects (say alcoholics and controls). It can also be used for single trial modeling, clinical classification of patients, and data filtering. The method is based on the topographic component model (TCM, Möcks 1988) which models brain potentials in a trilinear form. We extend the TCM in two aspects. First, the diagonal amplitude matrix is replaced by a general loading matrix based on some neurophysiological considerations. Secondly, the number of spatial components and the number of temporal components can be different. The spatial components and temporal components are obtained respectively by performing singular value decomposition (SVD). This method is illustrated with visual P3 data.

Brain mapping Event-related potentials Topographic component model Trilinear modeling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Achim, A. and Bouchard, S. Toward a dynamic topographic components model. Electroenceph. Clin. Neurophys., 1997, 103: 381-385.Google Scholar
  2. Bell, A. and Sejnowski, T. An information-maximization approach to blind separation and blind deconvolution. Neural Comp., 1995, 7: 1129-1159.Google Scholar
  3. Donchin, E. and Heffley, E. Multivariate analysis of event-related potential data: A tutorial review. In: D. Otto (Ed.), Multidisciplinary perspectives in event-related brain potential research, U.S. Gov. Printing Office, Washington DC, 1978: 555-572.Google Scholar
  4. Field, S. and Graupe, D. Topographic components analysis of evoked potentials: estimation of model parameters and evaluation of parameter uniqueness. J. Biomed. Eng., 1990, 12: 287-300.Google Scholar
  5. Field, S. and Graupe, D. Topographic component (parallel factor) analysis of multichannel evoked potentials: practical issues in trilinear spatiotemporal decomposition. Brain Topography, 1991, 3: 407-423.Google Scholar
  6. Glaser, E. and Ruchkin, D. Principles of neurobiological signal analysis. Academic Press, New York, 1976: 233:290.Google Scholar
  7. Harner, R. Singular value decomposition-a general linear model for analysis of multivariate structure in the electroencephalogram. Brain Topography, 1990, 3: 43-47.Google Scholar
  8. John, E., Ruchkin, D. and Villegas, J. Experimental background: signal analysis and behavioral correlations of evoked potential configuration in cats. Ann. N.Y. Acad. Sci., 1964, 112: 362-420.Google Scholar
  9. Makeig, S., Bell, A., Jung, T. and Sejnowski, T. Independent component analysis of electroencephalographic data. In: D. Touretzky, M. Mozer and M. Hasselmo (Eds.), Advances in neural info. proc. sys. 8, MIT Press, Cambridge MA, 1996: 145-151.Google Scholar
  10. Meyer, Y. Wavelets Algorithms & Applications. SIAM, Philadelphia, 1993.Google Scholar
  11. Mocks, J. Topographic components model for event-related potentials and some biophysical considerations. IEEE Trans. Biomed. Eng., 1988, 35: 482-484.Google Scholar
  12. Samar, V., Begleiter, H., Chapa, J., Raghuveer, M., Orlando, M. and Chorlian, D. Matched Meyer neural wavelets for clinical and experimental analysis of auditory and visual evoked potentials. Proceeding of the VIII European signal processing conference (EUSIPCO-96), Trieste, Sept. 1996: 10-13.Google Scholar
  13. Samar, V., Swartz, K. and Raghuveer, M. Multiresolution analysis of event-related potentials by wavelet decomposition. Brain and Cognition, 1995, 27: 398-438.Google Scholar
  14. Turetsky, B., Raz, J. and Fein, G. Representation of multichannel evoked potential data using a dipole component model of intracranial generators: application to the auditory P300. Electroenceph. Clin. Neurophys., 1990, 76: 540-556.Google Scholar
  15. Wang, K. and Begleiter, H. Local polynomial estimate of surface Laplacian. Brain Topography, 1999, 12: 19-29.Google Scholar
  16. Wang, K., Begleiter, H. and Porjesz, B. Spatial enhancement of event-related potentials using multiresolution analysis. Brain Topography, 1998, 10: 191-200.Google Scholar

Copyright information

© Human Sciences Press, Inc. 2000

Authors and Affiliations

  • Kongming Wang
    • 1
  • Henri Begleiter
    • 1
  • Bernice Porjesz
    • 1
  1. 1.Neurodynamics Laboratory, Department of PsychiatrySUNY Health Science Center at BrooklynBrooklynUSA

Personalised recommendations