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September 2018 Topological data analysis of single-trial electroencephalographic signals
Yuan Wang, Hernando Ombao, Moo K. Chung
Ann. Appl. Stat. 12(3): 1506-1534 (September 2018). DOI: 10.1214/17-AOAS1119

Abstract

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.

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Yuan Wang. Hernando Ombao. Moo K. Chung. "Topological data analysis of single-trial electroencephalographic signals." Ann. Appl. Stat. 12 (3) 1506 - 1534, September 2018. https://doi.org/10.1214/17-AOAS1119

Information

Received: 1 September 2016; Revised: 1 June 2017; Published: September 2018
First available in Project Euclid: 11 September 2018

zbMATH: 06979640
MathSciNet: MR3852686
Digital Object Identifier: 10.1214/17-AOAS1119

Keywords: electroencephalogram , Epilepsy , Persistence landscape , Persistent homology , weighted Fourier series

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.12 • No. 3 • September 2018
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