Topological data analysis of single-trial electroencephalographic signals

Abstract

Epilepsy is a neurological disorder that can negatively affect the visual, audial and motor functions of the human brain. Statistical analysis of neurophysiological recordings, such as electroencephalogram (EEG), facilitates the understanding and diagnosis of epileptic seizures. Standard statistical methods, however, do not account for topological features embedded in EEG signals. In the current study, we propose a persistent homology (PH) procedure to analyze single-trial EEG signals. The procedure denoises signals with a weighted Fourier series (WFS), and tests for topological difference between the denoised signals with a permutation test based on their PH features persistence landscapes (PL). Simulation studies show that the test effectively identifies topological difference and invariance between two signals. In an application to a single-trial multichannel seizure EEG dataset, our proposed PH procedure was able to identify the left temporal region to consistently show topological invariance, suggesting that the PH features of the Fourier decomposition during seizure is similar to the process before seizure. This finding is important because it could not be identified from a mere visual inspection of the EEG data and was in fact missed by earlier analyses of the same dataset.

Evaluating state space discovery by persistent cohomology in the spatial representation system

“…analysis of EEG signals, for classification and detection of epileptic seizures [36,37] and for construction of functional networks in a mouse model of depression [38]; inferring intrinsic geometric structure in neural activity [39]; and detection of coordinated behavior between human agents [40]. There is potential for persistent (co)homology to provide insight to a wide range of neural systems.…”

Detecting Traffic Incidents Using Persistence Diagrams

“…TDA has been applied previously to study time-series data in a variety of settings [33,34]. Existing applications include to financial data [35][36][37], medical signal (EEG) analysis [38,39] and general techniques including sliding-window methods [40][41][42][43]. Most of these methods rely on a Takens-style embedding to transform time-series data into point-cloud data [44,45].…”

Topological Learning for Brain Networks

“…Topological Data Analysis (TDA) (Edelsbrunner et al, 2000;Wasserman, 2018), a general framework based on algebraic topology, can provide such novel solution to the long-standing multimodal brain network analysis challenge. Numerous TDA studies have been applied to increasingly diverse problems such as genetics (Chung et al, 2017b(Chung et al, , 2019b, epileptic seizure detection (Wang et al, 2018), sexual dimorphism in the human brain (Songdechakraiwut and Chung, 2020), analysis of brain arteries (Bendich et al, 2016), image segmentation (Clough et al, 2019), classification (Singh et al, 2014;Reininghaus et al, 2015;Chen et al, 2019), clinical predictive model (Crawford et al, 2020) and persistencebased clustering (Chazal et al, 2013). Persistent homology begins to emerge as a powerful mathematical representation to understand, characterize and quantify topology of brain networks (Lee et al, 2012;Chung et al, 2019b).…”