Construction of Sparse Weighted Directed Network (SWDN) from the Multivariate Time-Series

  • Rahilsadat HosseiniEmail author
  • Feng Liu
  • Shouyi Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11309)


There are many studies focusing on network detection in multivariate (MV) time-series data. A great deal of focus have been on estimation of brain networks using functional Magnetic Resonance Imaging (fMRI), functional Near-Infrared Spectroscopy (fNIRS) and electroencephalogram (EEG). We present a sparse weighted directed network (SWDN) estimation approach which can detect the underlying minimum spanning network with maximum likelihood and estimated weights based on linear Gaussian conditional relationship in the MV time-series. Considering the brain neuro-imaging signals as the multivariate data, we evaluated the performance of the proposed approach using the publicly available fMRI data-set and the results of the similar study which had evaluated popular network estimation approaches on the simulated fMRI data.


Multivariate time-series Sparse weighted directed network (SWDN) fMRI 


  1. 1.
    Lacasa, L., Nicosia, V., Latora, V.: Network structure of multivariate time series. Sci. Rep. 5, Article no. 15508 (2015)Google Scholar
  2. 2.
    Hu, Y., Zhao, H., Ai, X.: Inferring weighted directed association network from multivariate time series with a synthetic method of partial symbolic transfer entropy spectrum and granger causality. PLOS ONE 11(11), 1–25 (2016)Google Scholar
  3. 3.
    Zhang, J., Small, M.: Complex network from pseudoperiodic time series: topology versus dynamics. Phys. Rev. Lett. 96, Article no. 238701 (2006)Google Scholar
  4. 4.
    Gutin, G., Mansour, T., Severini, S.: A characterization of horizontal visibility graphs and combinatorics on words. Phys. A Stat. Mech. Appl. 390(12), 2421–2428 (2011)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Anacleto, O., Queen, C., Albers, C.J.: Multivariate forecasting of road traffic flows in the presence of heteroscedasticity and measurement errors. J. R. Stat. Society. Ser. C (Appl. Stat.) 62(2), 251–270 (2013)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Zhao, Z.Y., Xie, M., West, M.: Dynamic dependence networks: financial time series forecasting and portfolio decisions. Appl. Stoch. Model. Bus. Ind. 32(3), 311–332 (2016). asmb.2161MathSciNetCrossRefGoogle Scholar
  7. 7.
    Siebenhhner, F., Weiss, S.A., Coppola, R., Weinberger, D.R., Bassett, D.S.: Intra- and inter-frequency brain network structure in health and schizophrenia. PLOS ONE 8(8), 1–13 (2013)Google Scholar
  8. 8.
    White, B.R., et al.: Resting-state functional connectivity in the human brain revealed with diffuse optical tomography. NeuroImage 47(1), 148–156 (2009)CrossRefGoogle Scholar
  9. 9.
    Im, C.-H., Jung, Y.-J., Lee, S., Koh, D., Kim, D.-W., Kim, B.-M.: Estimation of directional coupling between cortical areas using near-infrared spectroscopy (NIRS). Opt. Express 18(6), 5730–5739 (2010)CrossRefGoogle Scholar
  10. 10.
    Yuan, Z.: Combining independent component analysis and granger causality to investigate brain network dynamics with fNIRS measurements. Biomed. Opt. Express 4(11), 2629–2643 (2013)CrossRefGoogle Scholar
  11. 11.
    Homae, F., et al.: Development of global cortical networks in early infancy. J. Neurosci. 30(14), 4877–4882 (2010)CrossRefGoogle Scholar
  12. 12.
    David, O.: fMRI connectivity, meaning and empiricism comments on: Roebroeck et al. The identification of interacting networks in the brain using fMRI: model selection, causality and deconvolution. NeuroImage 58(2), 306–309 (2011)CrossRefGoogle Scholar
  13. 13.
    Deshpande, G., Sathian, K., Hu, X.: Assessing and compensating for zero-lag correlation effects in time-lagged granger causality analysis of fMRI. IEEE Trans. Biomed. Eng. 57(6), 1446–1456 (2010)CrossRefGoogle Scholar
  14. 14.
    Friston, K.: Dynamic causal modeling and granger causality comments on: the identification of interacting networks in the brain using fMRI: model selection, causality and deconvolution. NeuroImage 58(2), 303–305 (2011)CrossRefGoogle Scholar
  15. 15.
    Smith, S.M., et al.: Network modelling methods for fMRI. NeuroImage 54(2), 875–891 (2011)CrossRefGoogle Scholar
  16. 16.
    van Dellen, E., et al.: Minimum spanning tree analysis of the human connectome. Hum. Brain Mapp. 39(6), 2455–2471 (2018)CrossRefGoogle Scholar
  17. 17.
    Stam, C.J., et al.: The relation between structural and functional connectivity patterns in complex brain networks. Int. J. Psychophysiol. 103, 149–160 (2016). Research on Brain Oscillations and Connectivity in A New Take-Off StateCrossRefGoogle Scholar
  18. 18.
    Stam, C.J., Tewarie, P., Van Dellen, E., van Straaten, E.C.W., Hillebrand, A., Van Mieghem, P.: The trees and the forest: characterization of complex brain networks with minimum spanning trees. Int. J. Psychophysiol. 92(3), 129–138 (2014)CrossRefGoogle Scholar
  19. 19.
    Tewarie, P., van Dellen, E., Hillebrand, A., Stam, C.J.: The minimum spanning tree: an unbiased method for brain network analysis. NeuroImage 104, 177–188 (2015)CrossRefGoogle Scholar
  20. 20.
    Shmuel, A., Yacoub, E., Chaimow, D., Logothetis, N.K., Ugurbil, K.: Spatio-temporal point-spread function of fMRI signal in human gray matter at 7 tesla. NeuroImage 35(2), 539–552 (2007)CrossRefGoogle Scholar
  21. 21.
    Tak, S., Kempny, A.M., Friston, K.J., Leff, A.P., Penny, W.D.: Dynamic causal modelling for functional near-infrared spectroscopy. NeuroImage 111(Supplement C), 338–349 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.University of Texas at ArlingtonArlingtonUSA

Personalised recommendations