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    Topological data analysis of single-trial electroencephalographic signals

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    euclid.aoas.1536652963.pdf
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    Type
    Article
    Authors
    Wang, Yuan
    Ombao, Hernando cc
    Chung, Moo K.
    KAUST Department
    Biostatistics Group
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2018-09-11
    Online Publication Date
    2018-09-11
    Print Publication Date
    2018-09
    Permanent link to this record
    http://hdl.handle.net/10754/631519
    
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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 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.
    Citation
    Wang Y, Ombao H, Chung MK (2018) Topological data analysis of single-trial electroencephalographic signals. The Annals of Applied Statistics 12: 1506–1534. Available: http://dx.doi.org/10.1214/17-AOAS1119.
    Sponsors
    Supported in part by NIH Brain Initiative Grant EB022856 Supported in part by NSF DMS, NSF SES and the KAUST Baseline Research Fund.
    Publisher
    Institute of Mathematical Statistics
    Journal
    The Annals of Applied Statistics
    DOI
    10.1214/17-AOAS1119
    Additional Links
    https://projecteuclid.org/euclid.aoas/1536652963
    ae974a485f413a2113503eed53cd6c53
    10.1214/17-AOAS1119
    Scopus Count
    Collections
    Articles; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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