The Annals of Applied Statistics

Topological data analysis of single-trial electroencephalographic signals

Yuan Wang, Hernando Ombao, and Moo K. Chung

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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.

Article information

Source
Ann. Appl. Stat., Volume 12, Number 3 (2018), 1506-1534.

Dates
Received: September 2016
Revised: June 2017
First available in Project Euclid: 11 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1536652963

Digital Object Identifier
doi:10.1214/17-AOAS1119

Mathematical Reviews number (MathSciNet)
MR3852686

Keywords
Persistence landscape persistent homology weighted Fourier series electroencephalogram epilepsy

Citation

Wang, Yuan; Ombao, Hernando; Chung, Moo K. Topological data analysis of single-trial electroencephalographic signals. Ann. Appl. Stat. 12 (2018), no. 3, 1506--1534. doi:10.1214/17-AOAS1119. https://projecteuclid.org/euclid.aoas/1536652963


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