Skip to main content

Topological Features of Electroencephalography are Robust to Re-referencing and Preprocessing

Abstract

Electroencephalography (EEG) is among the most widely diffused, inexpensive, and adopted neuroimaging techniques. Nonetheless, EEG requires measurements against a reference site(s), which is typically chosen by the experimenter, and specific pre-processing steps precede analyses. It is therefore valuable to obtain quantities that are minimally affected by reference and pre-processing choices. Here, we show that the topological structure of embedding spaces, constructed either from multi-channel EEG timeseries or from their temporal structure, are subject-specific and robust to re-referencing and pre-processing pipelines. By contrast, the shape of correlation spaces, that is, discrete spaces where each point represents an electrode and the distance between them that is in turn related to the correlation between the respective timeseries, was neither significantly subject-specific nor robust to changes of reference. Our results suggest that the shape of spaces describing the observed configurations of EEG signals holds information about the individual specificity of the underlying individual’s brain dynamics, and that temporal correlations constrain to a large degree the set of possible dynamics. In turn, these encode the differences between subjects’ space of resting state EEG signals. Finally, our results and proposed methodology provide tools to explore the individual topographical landscapes and how they are explored dynamically. We propose therefore to augment conventional topographic analyses with an additional—topological—level of analysis, and to consider them jointly. More generally, these results provide a roadmap for the incorporation of topological analyses within EEG pipelines.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Data Availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

References

  • Bari S, Amico E, Vike N, Talavage TM, Goñi J (2019) Uncovering multi-site identifiability based on resting-state functional connectomes. NeuroImage 202:115967

    Article  Google Scholar 

  • Bassett DS, Sporns O (2017) Network neuroscience. Nat Neurosci 20(3):353–364

    CAS  Article  Google Scholar 

  • Battiston F, Cencetti G, Iacopini I, Latora V, Lucas M, Patania A, Young JG, Petri G (2020) Networks beyond pairwise interactions: structure and dynamics. Phys Rep 874:1–892

  • Betzel RF, Byrge L, He Y, Goñi J, Zuo XN, Sporns O (2014) Changes in structural and functional connectivity among resting-state networks across the human lifespan. NeuroImage 102:345–357

    Article  Google Scholar 

  • Biasiucci A, Franceschiello B, Murray MM (2019) Electroencephalography. Curr Biol 29(3):R80–R85. https://doi.org/10.1016/j.cub.2018.11.052

    CAS  Article  PubMed  Google Scholar 

  • Billings J, Saggar M, Hlinka J, Keilholz S, Petri G (2021) Simplicial and topological descriptions of human brain dynamics. Netw Neurosci. https://doi.org/10.1162/netn_a_00190

  • Cavanna NJ, Jahanseir M, Sheehy D (2015) A geometric perspective on sparse filtrations. In: Proceedings of the 27th Canadian conference on computational geometry, CCCG 2015, Kingston, Ontario, Canada, August 10–12, 2015, Queen’s University, Ontario, Canada

  • Chan HL, Kuo PC, Cheng CY, Chen YS (2018) Challenges and future perspectives on electroencephalogram-based biometrics in person recognition. Front Neuroinform 12:66. https://doi.org/10.3389/fninf.2018.00066

  • Chella F, Pizzella V, Zappasodi F, Marzetti L (2016) Impact of the reference choice on scalp EEG connectivity estimation. J Neural Eng 13(3):36016

    Article  Google Scholar 

  • Delorme A, Makeig S (2004) EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis. J Neurosci Methods 134(1):9–21

    Article  Google Scholar 

  • Deyle ER, Sugihara G (2011) Generalized theorems for nonlinear state space reconstruction. PLoS ONE 6(3):e18295. https://doi.org/10.1371/journal.pone.0018295

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  • Donato I, Gori M, Pettini M, Petri G, De Nigris S, Franzosi R, Vaccarino F (2016) Persistent homology analysis of phase transitions. Phys Rev E 93(5):52138

    Article  Google Scholar 

  • Edelsbrunner H, Harer J (2008) Persistent homology—a survey. Contemp Math 453:257–282

    Article  Google Scholar 

  • Fulekar MH (2009) Bioinformatics: applications in life and environmental sciences. Springer Science & Business Media, Boston

    Book  Google Scholar 

  • Ghrist R (2008) Barcodes: The persistent topology of data. https://doi.org/10.1090/S0273-0979-07-01191-3

  • Giusti C, Pastalkova E, Curto C, Itskov V (2015) Clique topology reveals intrinsic geometric structure in neural correlations. Proc Natl Acad Sci USA 112(44):13455–13460

    CAS  Article  Google Scholar 

  • Giusti C, Ghrist R, Bassett DS (2016) Twos company, three (or more) is a simplex. J Comput Neurosci 41(1):1–14

    Article  Google Scholar 

  • Grave de Peralta Menendez R, Gonzalez Andino S, Morand S, Michel C, Landis T (2000) Imaging the electrical activity of the brain: ELECTRA. Hum Brain Mapp 9(1):1–12

    CAS  Article  Google Scholar 

  • Haufe S, Ewald A (2019) A simulation framework for benchmarking EEG-based brain connectivity estimation methodologies. Brain Topogr 32(4):625–642

    Article  Google Scholar 

  • Hu S, Yao D, Bringas-Vega ML, Qin Y, Valdes-Sosa PA (2019) The statistics of eeg unipolar references: derivations and properties. Brain Topogr 32(4):696–703

    Article  Google Scholar 

  • Hutchison RM, Womelsdorf T, Allen EA, Bandettini PA, Calhoun VD, Corbetta M, Della Penna S, Duyn JH, Glover GH, Gonzalez-Castillo J et al (2013) Dynamic functional connectivity: promise, issues, and interpretations. NeuroImage 80:360–378

    Article  Google Scholar 

  • Iacopini I, Petri G, Barrat A, Latora V (2019) Simplicial models of social contagion. Nat Commun 10(1):1–9

    Article  Google Scholar 

  • Ibáñez-Marcelo E, Campioni L, Manzoni D, Santarcangelo EL, Petri G (2019a) Spectral and topological analyses of the cortical representation of the head position: does hypnotizability matter? Brain Behav 9(6):e01277

    Article  Google Scholar 

  • Ibáñez-Marcelo E, Campioni L, Phinyomark A, Petri G, Santarcangelo EL (2019b) Topology highlights mesoscopic functional equivalence between imagery and perception: the case of hypnotizability. NeuroImage 200:437–449

    Article  Google Scholar 

  • Kelley K, Preacher KJ (2012) On effect size. Psychol Methods 17(2):137

    Article  Google Scholar 

  • Lee S, Kang H, Chung MK, Kim BN, Lee DS (2012) Persistent brain network homology from the perspective of dendrogram. IEEE Trans Med Imaging 31(12):2267–2277

    Article  Google Scholar 

  • Lehmann D (1987) Principles of spatial analysis. In: Gevins A, Rémond A (eds) Handbook of electroencephalography and clinical neurophysiology: methods of analysis of brain electrical and magnetic signals, vol 1. Elsevier, Amsterdam, pp 309–354

  • Lehmann D, Michel CM (2011) EEG-defined functional microstates as basic building blocks of mental processes. Clin Neurophysiol 122(6):1073–1074. https://doi.org/10.1016/j.clinph.2010.11.003

  • Leon PS, Knock SA, Woodman MM, Domide L, Mersmann J, McIntosh AR, Jirsa V, Marinazzo D, Plesser HE (2013) The virtual brain: a simulator of primate brain network dynamics. Front Neuroinform. https://doi.org/10.3389/fninf.2013.00010

  • Lepage KQ, Kramer MA, Chu CJ (2014) A statistically robust EEG re-referencing procedure to mitigate reference effect. J Neurosci Methods 235:101–116. https://doi.org/10.1016/j.jneumeth.2014.05.008

  • Luck SJ (2014) An introduction to the event-related potential technique. A Bradford book. MIT Press. https://books.google.com/books?id=SzavAwAAQBAJ

  • Marcel S, Millan JDR (2007) Person authentication using brainwaves (EEG) and maximum a posteriori model adaptation. IEEE Trans Pattern Anal Mach Intell 29(4):743–752

    Article  Google Scholar 

  • Marinazzo D, Riera JJ, Marzetti L et al (2019) Controversies in EEG source imaging and connectivity: modeling, validation, benchmarking. Brain Topogr 32:527–529. https://doi.org/10.1007/s10548-019-00709-9

    Article  PubMed  Google Scholar 

  • Michel CM, Murray MM (2012) Towards the utilization of EEG as a brain imaging tool. NeuroImage 61(2):371–385. https://doi.org/10.1016/j.neuroimage.2011.12.039

  • Michel CM, Thut G, Morand S, Khateb A, Pegna AJ, Grave de Peralta R, Gonzalez S, Seeck M, Landis T (2001) Electric source imaging of human brain functions. Brain Res Rev 36(2):108–118. https://doi.org/10.1016/S0165-0173(01)00086-8

  • Michel CM, Murray MM, Lantz G, Gonzalez S, Spinelli L, Grave de Peralta R (2004) EEG source imaging. Clin Neurophysiol 115(10):2195–2222. https://doi.org/10.1016/j.clinph.2004.06.001

  • Michel CM, Koenig T, Brandeis D, Gianotti LR, Wackermann J (2009) Electrical neuroimaging. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511596889

    Book  Google Scholar 

  • Murray MM, Brunet D, Michel CM (2008) Topographic ERP analyses: a step-by-step tutorial review. Brain Topogr 20(4):249–264. https://doi.org/10.1007/s10548-008-0054-5

    Article  PubMed  Google Scholar 

  • Myers A, Munch E, Khasawneh FA (2019) Persistent homology of complex networks for dynamic state detection. Phys Rev E 100(2):22314

    CAS  Article  Google Scholar 

  • Noakes L (1991) The Takens embedding theorem. Int J Bifurcat Chaos 1(04):867–872

    Article  Google Scholar 

  • Perrin F, Pernier J, Bertrand O, Echallier JF (1989) Spherical splines for scalp potential and current density mapping. Electroencephalogr Clin Neurophysiol 72(2):184–187

    CAS  Article  Google Scholar 

  • Petri G, Scolamiero M, Donato I, Vaccarino F (2013) Topological strata of weighted complex networks. PLoS ONE 8(6):e66506

    CAS  Article  Google Scholar 

  • Petri G, Expert P, Turkheimer F, Carhart-Harris R, Nutt D, Hellyer PJ, Vaccarino F (2014) Homological scaffolds of brain functional networks. J R Soc Interface 11(101):20140873

  • Poulos M, Rangoussi M, Alexandris N (1999) Neural network based person identification using EEG features. In: Proceedings—1999 IEEE international conference on acoustics, speech, and signal processing, vol 2. ICASSP99 (Cat. No. 99CH36258), IEEE, pp 1117–1120

  • Rajapandian M, Amico E, Abbas K, Ventresca M, Goñi J (2020) Uncovering differential identifiability in network properties of human brain functional connectomes. Netw Neurosci 4(3):698–713

    Article  Google Scholar 

  • Reininghaus J, Huber S, Bauer U, Kwitt R (2015) A stable multi-scale kernel for topological machine learning. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 4741–4748

  • Sakkalis V (2011) Review of advanced techniques for the estimation of brain connectivity measured with EEG/MEG. Comput Biol Med 41(12):1110–1117

    CAS  Article  Google Scholar 

  • Sawilowsky SS (2009) New effect size rules of thumb. J Mod Appl Stat Methods 8(2):26

    Article  Google Scholar 

  • Schirner M, Domide L, Perdikis D, Triebkorn P, Stefanovski L, Pai R, Popa P, Valean B, Palmer J, Langford C, Blickensdörfer A, van der Vlag M, Diaz-Pier S, Peyser A, Klijn W, Pleiter D, Nahm A, Schmid O, Woodman M, Zehl L, Fousek J, Petkoski S, Kusch L, Hashemi M, Marinazzo D, Mangin JF, Flöel A, Akintoye S, Stahl BC, Cepic M, Johnson E, Deco G, McIntosh AR, Hilgetag CC, Morgan M, Schuller B, Upton A, McMurtrie C, Dickscheid T, Bjaalie JG, Amunts K, Mersmann J, Jirsa V, Ritter P (2021) Brain modelling as a service: the virtual brain on EBRAINS. arXiv preprint. http://arxiv.org/abs/2102.05888

  • Sporns O (2013) Network attributes for segregation and integration in the human brain. Curr Opin Neurobiol 23(2):162–171

    CAS  Article  Google Scholar 

  • Tenke CE, Kayser J (2005) Reference-free quantification of EEG spectra: combining current source density (CSD) and frequency principal components analysis (fPCA). Clin Neurophysiol 116(12):2826–2846

    Article  Google Scholar 

  • Tivadar RI, Retsa C, Turoman N, Matusz PJ, Murray MM (2018) Sounds enhance visual completion processes. NeuroImage 179:480–488

    Article  Google Scholar 

  • Tivadar RI, Murray MM, Tivadar RI, Murray MM (2019) A primer on electroencephalography and event-related potentials for organizational neuroscience. Organ Res Methods 22(1):69–94. https://doi.org/10.1177/1094428118804657

  • Varley TF, Denny V, Sporns O, Patania A (2020) Topological analysis of differential effects of ketamine and propofol anesthesia on brain dynamics. bioRxiv

  • Vaughan HG (1982) The neural origins of human event-related potentials. Ann N Y Acad Sci 388(1):125–138

  • Wong PKH (2012) Introduction to brain topography. Springer Science & Business Media, Boston

    Google Scholar 

  • Yao D, Qin Y, Hu S, Dong L, Vega M, Sosa PAV (2019) Which reference should we use for EEG and ERP practice? Brain Topogr 32(4):530–549. https://doi.org/10.1007/s10548-019-00707-x

  • Zomorodian A, Carlsson G (2005) Computing persistent homology. Discrete Comput Geom 33(2):249–274

    Article  Google Scholar 

Download references

Funding

B.F. and M.M.M. are supported by the Fondation Asile des aveugles (Grant Number 232933 to M.M.M.). M.M.M. is also supported by The Swiss National Science Foundation (Grant Number 169206). R.T. is supported by the Swiss National Science Foundation (#320030_188737). G.P. and J.B. acknowledge support during the preparation of this work from Intesa Sanpaolo Innovation Center. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Author information

Authors and Affiliations

Authors

Contributions

MMM, BF and GP conceived the study. RT gathered and pre-processed the data. JB structured and carried out the topological data analysis over the three embedding types. BF, GP, JB and RT interpreted together the results. RT and JB wrote the first draft of the manuscript. BF supervised the neuroscientific contents and GP the topological ones. All authors contributed to the final draft and review.

Corresponding author

Correspondence to Giovanni Petri.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Handling Editor: Jeremie Lefebvre.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This is one of several papers published together in Brain Topography on the “Special Issue: Computational Modeling and M/EEG”.

Supplementary Information

Appendix

Appendix

Results for Additional Preprocessing Pipelines

See Figs. 6, 7, and 8.

Fig. 6
figure 6

Effect of different preprocessing pipelines on correlation spaces \(X^{s,r}\). Additional pipeline results for Fig. 3: (top row) clean pipeline. (middle row) filtered pipeline. (bottom row) tvb pipeline

Fig. 7
figure 7

Effect of different preprocessing pipelines on Takens embedding spaces \(T^{s,r}\). Additional pipeline results for Fig. 3: (top row) clean pipeline. (middle row) filtered pipeline. (bottom row) tvb pipeline

Fig. 8
figure 8

Effect of different preprocessing pipelines on direct temporal embedding spaces \(D^{s,r}\). Additional pipeline results for Fig. 3: (top row) clean pipeline. (middle row) filtered pipeline. (bottom row) tvb pipeline

Results for \(T^{s,r}\) Spaces from Temporally Shuffled Timeseries

See Fig. 9.

Fig. 9
figure 9

Effect for temporally reshuffled timeseries for clean, filtered, and tvb pipelines

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Billings, J., Tivadar, R., Murray, M.M. et al. Topological Features of Electroencephalography are Robust to Re-referencing and Preprocessing. Brain Topogr 35, 79–95 (2022). https://doi.org/10.1007/s10548-021-00882-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10548-021-00882-w

Keywords

  • Resting-state electroencephalography
  • Topography
  • Topology
  • Network
  • Computational modelling
  • Reference electrode