Topological data analysis of single-trial electroencephalographic signals

Yuan Wang, Hernando Ombao, Moo K. Chung

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


Epilepsy is a neurological disorder marked by sudden recurrent episodes of sensory disturbance, loss of consciousness, or convulsions, associated with abnormal electrical activity in the brain. Statistical analysis of neuro-physiological recordings, such as electroencephalography (EEG), facilitates the understanding of epileptic seizures. Standard statistical methods typically analyze amplitude and frequency information in EEG signals. In the current study, we propose a topological data analysis (TDA) framework to analyze single-trial EEG signals. The framework denoises signals with a weighted Fourier series (WFS), and tests for differences between the topological features—persistence landscapes (PLs) of denoised signals through resampling in the frequency domain. Simulation studies show that the test is robust for topologically similar signals while bearing sensitivity to topological tearing in signals. In an application to single-trial epileptic EEG signals, EEG signals in the diagnosed seizure origin and its symmetric site are found to have similar PLs before and during a seizure attack, in contrast to signals at other sites showing significant statistical difference in the PLs of the two phases.

Original languageEnglish (US)
Pages (from-to)1506-1534
Number of pages29
JournalAnnals of Applied Statistics
Issue number3
StatePublished - Sep 2018


  • Electroencephalogram
  • Epilepsy
  • Persistence landscape
  • Persistent homology
  • Weighted fourier series

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Modeling and Simulation


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