Topological recurrence in EEG dynamics: A complementary, wake-to-REM-graded descriptor of sleep-stage organisation - 30/08/26
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Highlights |
• | K 0 is a topological EEG descriptor of sleep-stage organisation. |
• | REM–Wake separation +1.01 SD, replicated in an independent cohort. |
• | Information statistically independent of band power and complexity measures. |
• | Robust across all 12 tested embedding parameters. |
• | Attenuates with age; invariant under benzodiazepine challenge. |
Abstract |
Background. Sleep-stage EEG analysis conventionally relies on spectral and complexity measures. Whether the geometric organisation of neural dynamics provides complementary information remains untested. Here I test whether a topological recurrence descriptor derived from persistent homology indexes a dimension of sleep-stage EEG organisation that is statistically distinct from spectral and complexity measures.
New method. K 0 , a within-subject z-scored summary of persistent homology of time-delay embeddings ( 
, 
) of single-channel frontal-midline (Fpz–Cz) EEG, was computed on 197 nights from 100 subjects (Sleep-EDF Expanded, a public polysomnography corpus). Mixed-effects models, binomial generalised linear models (GLMs), and leave-one-subject-out classification benchmarked K 0 against band power, spectral entropy, permutation entropy, and Lempel–Ziv complexity.
Results. K 0 , varying systematically across sleep stages, is statistically distinct from spectral content (Pearson r 
to 
with log band powers; opposite rapid eye movement (REM)–Wake direction), with construct validity supported by independent-cohort replication, twofold lifespan attenuation, and within-subject benzodiazepine invariance. The REM–Wake separation is large ( 
standard deviation (SD); 
) and preserved across embeddings.
Comparison with existing methods. A binomial GLM confirms K 0 carries information statistically independent of band power, especially for REM vs active-ocular wake (ΔAkaike Information Criterion (AIC) 
, odds ratio (OR) 
). Leave-one-subject-out area under the receiver operating characteristic curve (AUC) values are 0.79 ( K 0 ) and 0.91 (band power); combining adds a small gain (ΔAUC 
, paired-bootstrap 
).
Conclusions. K 0 is a topologically distinct, spectrally non-redundant descriptor of sleep-stage EEG organisation.
Il testo completo di questo articolo è disponibile in PDF.Keywords : Persistent homology, Topological data analysis, Sleep EEG, REM sleep, State-space reconstruction, Sleep-EDF
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Vol 6 - N° 4
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