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.

Cognitive Computational Neuroscience Group Institute for Computer Science University of Bern Bern Switzerland

Department of Complex Systems Institute for Computer Science Czech Academy of Science Prague Czechia

Department of Hearing and Speech Sciences Vanderbilt University Nashville TN USA

Department of Ophthalmology Fondation Asile des aveugles and University of Lausanne Lausanne Switzerland

EEG CHUV UNIL Section CIBM Center for Biomedical Imaging Lausanne Switzerland

ISI Foundation Turin Italy

ISI Global Science Foundation New York NY USA

Laboratory for Investigative Neurophysiology Department of Radiology Lausanne University Hospital and University of Lausanne Lausanne Switzerland

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

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

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 DOI

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

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 DOI

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 DOI

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 PubMed DOI PMC

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 DOI

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

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

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 DOI

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

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 DOI

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

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 DOI

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 DOI

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

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 DOI

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 DOI

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

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 DOI

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 DOI

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 PubMed DOI

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 DOI

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 PubMed DOI

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

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

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 DOI

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

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 DOI

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 DOI

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

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 DOI

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 DOI

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

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

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 DOI