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A Scaled-Correlation Based Approach for Defining and Analyzing Functional Networks

  • Samuel Dolean
  • Mihaela Dînşoreanu
  • Raul Cristian Mureşan
  • Attila Geiszt
  • Rodica Potolea
  • Ioana Ţincaş
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10785)

Abstract

Many natural systems can be described as networks of interacting elements, forming a graph of interactions. This is the case for climate models, coupled chemical systems, computer or social networks, or the brain. For many of these cases, dynamical networks emerge whose structure changes in time. Estimating the structure of such networks from the time series that describe the activity of their nodes is a serious challenge. Here, we devise a new method that is based on the Scaled Correlation function to estimate interactions between nodes that occur on fast timescales. We apply the method on EEG measurements from human volunteers to evaluate neuronal functional connectivity associated with a visual perception task. We compare the statistics of networks extracted with the new method with those that are extracted using traditional techniques, like the Pearson correlation coefficient or the cross-correlation function. Results indicate that the new method is superior in identifying networks whose structure correlates to the cognitive processes engaged during visual perception. The method is general enough to be applied on any data that describes dynamical interactions evolving on multiple timescales, as is the case in climate modeling, chemical networks, or complex biological systems.

Keywords

EEG Functional brain networks Metrics Cross-Correlation Scaled-Correlation Pearson correlation coefficient Directed weighted network 

Notes

Acknowledgement

This work was supported by two grants from Consiliul National al Cercetării Ştiinţifice (CNCS) - Unitatea Executivă pentru Finanţarea Învăţământului Superior, a Cercetării Dezvoltării şi Inovării (UEFISCDI): PNII-RU-TE-2014-4- 13 0406/2015 contract no. 169/2015 and PN-III-P4-ID-PCE-2016-0010 contract no. 78/2017.

References

  1. 1.
    Barabasi, A.L.: Network Science. Cambridge University Press, Cambridge (2016)zbMATHGoogle Scholar
  2. 2.
    Koniaris, M., Anagnostopoulos, I., Vassiliou, Y.: Network analysis in the legal domain: a complex model for European Union legal sources, CoRR (2015)Google Scholar
  3. 3.
    Baggio, R., Scott, N., Cooper, C.: Network science: a review focused on tourism. Ann. Tour. Res. 37, 802–827 (2010)CrossRefGoogle Scholar
  4. 4.
    Bullmore, E., Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10(4), 312 (2009)CrossRefGoogle Scholar
  5. 5.
    Lange, S., Donges, J.F., Volkholz, J., Kurths, J.: Local difference measures between complex networks for dynamical system model evaluation. PLoS ONE 10(4), e0129413 (2015)CrossRefGoogle Scholar
  6. 6.
    Pearson, K.: Notes on regression and inheritance in the case of two parents. Proc. Royal Soc. Lond. 58, 240–242 (1895)CrossRefGoogle Scholar
  7. 7.
    Bracewell, R.: Pentagram notation for cross correlation. In: The Fourier Transform and Its Applications, pp. 46 and 243. McGraw-Hill, New York (1965)Google Scholar
  8. 8.
    Nikolić, D., Mureşan, R.C., Feng, W., Singer, W.: Scaled correlation analysis: a better way to compute a cross-correlogram. Eur. J. Neurosci. 35(5), 742–762 (2012)CrossRefGoogle Scholar
  9. 9.
    Friston, K.J.: Functional and effective connectivity: a review. Brain Connect. 1(1), 13–36 (2011)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Park, H.J., Friston, K.: Structural and functional brain networks: from connections to cognition. Science 342(6158), 1238411 (2013)CrossRefGoogle Scholar
  11. 11.
    Rubinov, M., Sporns, O.: Complex network measures of brain connectivity: uses and interpretations. NeuroImage 52(3), 1059–1069 (2010). Computational Models of the BrainCrossRefGoogle Scholar
  12. 12.
    Finc, K., Bonna, K., Lewandowska, M., Wolak, T., Nikadon, J., Dreszer, J., Duch, W., Khn, S.: Transition of the functional brain network related to increasing cognitive demands. Hum. Brain Mapp. 38, 3659–3674 (2017)Google Scholar
  13. 13.
    Joudaki, A., Salehi, N., Jalili, M., Knyazeva, M.G.: EEG based functional brain networks: does the network size matter? PLoS ONE 7(4), 1–9 (2012)CrossRefGoogle Scholar
  14. 14.
    Jalili, M., Knyazeva, M.G.: Constructing brain functional networks from EEG: partial and unpartial correlations. J. Integr. Neurosci. 10(2), 213–232 (2011)CrossRefGoogle Scholar
  15. 15.
    Meador, K.J., Ray, P.G.: Gamma frequency coherence and conscious perception. J. Clin. Neurophysiol. 16(2), 170 (1999)CrossRefGoogle Scholar
  16. 16.
    Bordier, C., Nicolini, C., Bifone, A.: Graph analysis and modularity of brain functional connectivity networks: searching for the optimal threshold. Front. Neurosci. 11, 441 (2017)CrossRefGoogle Scholar
  17. 17.
    Opsahl, T., Agneessens, F., Skvoretz, J.: Node centrality in weighted networks: generalizing degree and shortest paths. Soc. Netw. 32(3), 245–251 (2010)CrossRefGoogle Scholar
  18. 18.
    Reppas, A.I., Spiliotis, K., Siettos, C.I.: Tuning the average path length of complex networks and its influence to the emergent dynamics of the majority-rule model. Math. Comput. Simul. 109, 186–196 (2015)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Opsahl, T., Panzarasa, P.: Clustering in weighted networks. Soci. Netw. 31(2), 155–163 (2009)CrossRefGoogle Scholar
  20. 20.
    Moca, V.V., Ţincaş, I., Melloni, L., Mureşan, R.C.: Visual exploration and object recognition by lattice deformation. PLoS ONE 6(7), e22831 (2011)CrossRefGoogle Scholar
  21. 21.
    Singer, W.: Neuronal synchrony: a versatile code for the definition of relations? Neuron 24(1), 49–65 (1999)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Fries, P., Nikolić, D., Singer, W.: The gamma cycle. Trends Neurosci. 30(7), 309–316 (2007)CrossRefGoogle Scholar
  23. 23.
    Stam, C.J.: Modern network science of neurological disorders. Nat. Rev. Neurosci. 15, 683–695 (2014)CrossRefGoogle Scholar
  24. 24.
    Jarosiewicz, B., Chase, S.M., Fraser, G.W., Velliste, M., Kass, R.E., Schwartz, A.B.: Functional network reorganization during learning in a brain-computer interface paradigm. Proc. Natl. Acad. Sci. U.S.A. 105(49), 19486–19491 (2008)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceTechnical University of Cluj-NapocaCluj-NapocaRomania
  2. 2.Transylvanian Institute of NeuroscienceCluj-NapocaRomania

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