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Topological data analysis of single-trial electroencephalographic signals. (English) Zbl 1405.62212

Summary: 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 neurophysiological 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.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62-07 Data analysis (statistics) (MSC2010)
55R40 Homology of classifying spaces and characteristic classes in algebraic topology
62H35 Image analysis in multivariate analysis
62G09 Nonparametric statistical resampling methods
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