Journal of Biological Physics

, Volume 34, Issue 3–4, pp 315–323 | Cite as

Identifying Complex Brain Networks Using Penalized Regression Methods

  • Eduardo Martínez-Montes
  • Mayrim Vega-Hernández
  • José M. Sánchez-Bornot
  • Pedro A. Valdés-Sosa
Original Paper


The recorded electrical activity of complex brain networks through the EEG reflects their intrinsic spatial, temporal and spectral properties. In this work we study the application of new penalized regression methods to i) the spatial characterization of the brain networks associated with the identification of faces and ii) the PARAFAC analysis of resting-state EEG. The use of appropriate constraints through non-convex penalties allowed three types of inverse solutions (Loreta, Lasso Fusion and ENet L) to spatially localize networks in agreement with previous studies with fMRI. Furthermore, we propose a new penalty based in the Information Entropy for the constrained PARAFAC analysis of resting EEG that allowed the identification in time, frequency and space of those brain networks with minimum spectral entropy. This study is an initial attempt to explicitly include complexity descriptors as a constraint in multilinear EEG analysis.


Information Entropy PARAFAC EEG inverse problem Multiple penalized least squares model Complex brain networks 



The authors thank Mark Cohen and Jhoanna Pérez-Hidalgo-Gato for kindly providing the data of the resting EEG and face identification experiment used in this study.


  1. 1.
    Pascual-Marqui, R.D.: Review of methods for solving the EEG inverse problem. Int. J. Bioelectromagn. 1, (1), 75–86 (1999)Google Scholar
  2. 2.
    Durka, P.J., Blinowska, K.J.: A unified time–frequency parametrization of EEG. IEEE Eng. Med. Biol. 20, (5), 47–53 (2001)CrossRefGoogle Scholar
  3. 3.
    Makeig, S., Westerfield, M., Jung, T.P., Enghoff, S., Townsend, J., Courchesne, E., Sejnowski, T.J.: Dynamic brain sources of visual evoked responses. Science 295, 690–694 (2002)CrossRefADSGoogle Scholar
  4. 4.
    Miwakeichi, F., Martínez-Montes, E., Valdés-Sosa, P.A., Nishiyama, N., Mizuhara, H., Yamaguchi, Y.: Decomposing EEG data into space–time–frequency components using Parallel Factor Analysis. Neuroimage 22, (3), 1035–1045 (2004)CrossRefGoogle Scholar
  5. 5.
    Harrison, L., Penny, W.D., Friston, K.: Multivariate autoregressive modeling of fmri time series. Neuroimage 19, 1477–1491 (2003)CrossRefGoogle Scholar
  6. 6.
    Freiwald, W.A., Valdés, P.A., Bosch, J., Biscay, R., Jiménez, J.C., Rodríguez, L.M., Kreiter, A.K., Singer, W.: Testing non-linearity and directness of interactions between neural groups in the macaque inferotemporal cortex. J. Neurosci. Methods 94, 105–119 (1999)CrossRefGoogle Scholar
  7. 7.
    Friston, K.J., Holmes, A.P., Worsley, K.J., Poline, J.P., Frith, C.D., Frackowiak, R.S.J.: Statistical parametric maps in functional imaging: a general linear approach. Hum. Brain Mapp. 2, (4), 189–210 (1994)CrossRefGoogle Scholar
  8. 8.
    Kiebel, S.J., Tallon-Baudry, C., Friston, K.J.: Parametric analysis of oscillatory activity as measured with EEG/MEG. Hum. Brain Mapp. 26, 170–177 (2005)CrossRefGoogle Scholar
  9. 9.
    Fan, J.Q., Li, R.Z.: Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Stat. Assoc. 96, 1348–1360 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Tibshirani, R.: Regression shrinkage and variable selection via the lasso. J. R. Stat. Soc. Ser. B 58, 267–288 (1996)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Zou, H., Hastie, T.: Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B 67, 301–320 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Hunter, D.R., Li, R.: Variable selection using MM algorithms. Ann. Stat. 33, 1617–1642 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Valdés-Sosa, P.A., Sánchez-Bornot, J.M., Vega-Hernández, M., Melie-García, L., Lage-Castellanos, A., Canales-Rodríguez, E.: Granger causality on spatial manifolds: applications to neuroimaging. In: Schelter, B., Winterhalter, M., Timmer, J. (eds.) Handbook of Time Series Analysis: Recent Theoretical Developments and Applications, pp. 461–492. Wiley-VCH, Weinheim (2006)Google Scholar
  14. 14.
    Land, S., Friedman, J.: Variable fusion: a new method of adaptive signal regression. Technical Report. Department of Statistics, Stanford University, Stanford (1996)Google Scholar
  15. 15.
    Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423, 623–656 (1948)zbMATHMathSciNetGoogle Scholar
  16. 16.
    Vega-Hernández, M., Sánchez-Bornot, J.M., Lage-Castellanos, A., Martínez-Montes, E., Valdés-Sosa, P.A.: Penalized regression methods for solving the EEG inverse problem. NeuroImage 27(1) (2006) (CD-ROM)Google Scholar
  17. 17.
    Golub, G.H., Heat, M., Wahba, G.: Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21, 215–223 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Bro, R.: Multi-way analysis in the food industry: Models, algorithms and applications. PhD thesis, University of Amsterdam and Royal Veterinary and Agricultural University, Denmark, (1998)Google Scholar
  19. 19.
    Martínez-Montes, E., Sánchez-Bornot, J.M., Valdés-Sosa, P.A.: Generalized penalized PARAFAC analysis of EEG time series. NeuroImage, 36(S1), (2007) (CD-ROM)Google Scholar
  20. 20.
    Mardia, K., Kent, J., Bibby, J.: Multivariate analysis. Academic Press, San Diego, CA (1979)zbMATHGoogle Scholar
  21. 21.
    Kanwisher, N., McDermott, J., Chon, M.M.: The fusiform area: a module in human extrastriate cortex specialized for face perception. J. Neurosci. 17, 4302–4311 (1997)Google Scholar
  22. 22.
    Martínez-Montes, E., Valdés-Sosa, P.A., Miwakeichi, F., Goldman, R.I., Cohen, M.S.: Concurrent EEG/fMRI analysis by multi-way partial least squares. NeuroImage 22, (3), 1023–1034 (2004)CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media B.V. 2008

Authors and Affiliations

  • Eduardo Martínez-Montes
    • 1
  • Mayrim Vega-Hernández
    • 1
  • José M. Sánchez-Bornot
    • 1
  • Pedro A. Valdés-Sosa
    • 1
  1. 1.Neurostatistics DepartmentCuban Neuroscience CenterHavanaCuba

Personalised recommendations