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


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.

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Data Availability

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


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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.

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Authors and Affiliations



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.

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Handling Editor: Jeremie Lefebvre.

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

Supplementary Information



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

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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).

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