Statistical Persistent Homology of Brain Signals

Wang, Yuan; Ombao, Hernando; Chung, Moo K.

doi:10.1109/icassp.2019.8682978

Cited by 20 publications

(7 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…During the filtration, the time when a k -dimensional hole appears in the simplicial complex is recorded as T start , while T end is the time when the k -dimensional hole disappears. Accordingly, the k -dimensional Betti interval is defined by [ T start , T end ], and the corresponding persistence barcode is its graphical representation of it [ 8 , 26 , 27 ]. On the other hand, persistent entropy (PE) provides a new entropy measure to extract the feature of topological space by persistence barcode.…”

Section: Experiments and Methods For Assessing Brain Cognition's Gestalt Patternsmentioning

confidence: 99%

Persistent Homology-Based Topological Analysis on the Gestalt Patterns during Human Brain Cognition Process

Liu

et al. 2021

Journal of Healthcare Engineering

View full text Add to dashboard Cite

The neuropsychological characteristics inside the brain are still not sufficiently understood in previous Gestalt psychological analyses. In particular, the extraction and analysis of human brain consciousness information itself have not received enough attention for the time being. In this paper, we aim to investigate the features of EEG signals from different conscious thoughts. Specifically, we try to extract the physiologically meaningful features of the brain responding to different contours and shapes in images in Gestalt cognitive tests by combining persistent homology analysis with electroencephalogram (EEG). The experimental results show that more brain regions in the frontal lobe are involved when the subject perceives the random and disordered combination of images compared to the ordered Gestalt images. Meanwhile, the persistence entropy of EEG data evoked by random sequence diagram (RSD) is significantly different from that evoked by the ordered Gestalt (GST) images in several frequency bands, which indicate that the human cognition of the shape and contour of images can be separated to some extent through topological analysis. This implies the feasibility to digitize the neural signals while preserving the whole and local features of the original signals, which are further verified by our extensive experiments. In general, this paper evaluates and quantifies cognitively related neural correlates by persistent homology features of EEG signals, which provides an approach to realizing the digitization of neural signals. Preliminary verification of the analyzability of human consciousness signals provides reliable research ideas and directions for the realization of feature extraction and analysis of human brain consciousness cognition.

show abstract

Section: Experiments and Methods For Assessing Brain Cognition's Gestalt Patternsmentioning

confidence: 99%

Persistent Homology-Based Topological Analysis on the Gestalt Patterns during Human Brain Cognition Process

Liu

et al. 2021

Journal of Healthcare Engineering

View full text Add to dashboard Cite

show abstract

“…The TDA technique adopts a persistent homology [56], [57] tool to describe the point clouds, providing a novel description of the structure of the point clouds and topological properties of the phase space. The nonlinear dynamics analysis with topological descriptions has been used in wheeze detection [58], heart dynamics analysis toward arrhythmia detection [59], gait dynamics analysis toward neurodegenerative disease discrimination [60], [61], EEG-based dynamics analysis toward brain state recognition [62], [63], [64], [65], [66], [67], [68], [69] and plenty of time series classification applications [70], [71], [72]. This work proposes a topological nonlinear dynamics analysis approach toward EEG-based emotion recognizing as a complement of the phase space information, namely topological EEG nonlinear dynamics analysis (TEEGNDA).…”

Section: Introductionmentioning

confidence: 99%

Topological EEG Nonlinear Dynamics Analysis for Emotion Recognition

Yan,

Wu,

et al. 2022

Preprint

View full text Add to dashboard Cite

Emotional recognition through exploring the electroencephalography (EEG) characteristics has been widely performed in recent studies. Nonlinear analysis and feature extraction methods for understanding the complex dynamical phenomena are associated with the EEG patterns of different emotions. The phase space reconstruction is a typical nonlinear technique to reveal the dynamics of the brain neural system. Recently, the topological data analysis (TDA) scheme has been used to explore the properties of space, which provides a powerful tool to think over the phase space. In this work, we proposed a topological EEG nonlinear dynamics analysis approach using the phase space reconstruction (PSR) technique to convert EEG time series into phase space, and the persistent homology tool explores the topological properties of the phase space. We perform the topological analysis of EEG signals in different rhythm bands to build emotion feature vectors, which shows high distinguishing ability. We evaluate the approach with two well-known benchmark datasets, the DEAP and DREAMER datasets. The recognition results achieved accuracies of 99.37% and 99.35% in arousal and valence classification tasks with DEAP, and 99.96%, 99.93%, and 99.95% in arousal, valence, and dominance classifications tasks with DREAMER, respectively. The performances are supposed to be outperformed current state-of-art approaches in DREAMER (improved by 1% to 10% depends on temporal length), while comparable to other related works evaluated in DEAP. The proposed work is the first investigation in the emotion recognition oriented EEG topological feature analysis, which brought a novel insight into the brain neural system nonlinear dynamics analysis and feature extraction.

show abstract

“…For example, the Vietoris-Rips (VR) complex filtration and the bottleneck or Wasserstein distances among persistence diagrams are applied to study voices and body motions (Seversky et al, 2016 ; Venkataraman et al, 2016 ). A transformation of the persistence diagram, called persistence landscapes (Bubenik, 2015 ), has been applied to study trading records (Gidea and Katz, 2018 ), electroencephalogram (EEG) signals (Piangerelli et al, 2018 ; Wang et al, 2018 ; Wang et al, 2019 ), and cryptocurrency trend forecasting (Kim et al, 2018 ). Sliding Windows and 1-Persistence Scoring (Perea, 2019 ) offers both theoretical and practical TDA method to detect the periodicity of a time series.…”

Section: Introductionmentioning

confidence: 99%

A Persistent Homology Approach to Heart Rate Variability Analysis With an Application to Sleep-Wake Classification

Chung

et al. 2021

Front. Physiol.

View full text Add to dashboard Cite

Persistent homology is a recently developed theory in the field of algebraic topology to study shapes of datasets. It is an effective data analysis tool that is robust to noise and has been widely applied. We demonstrate a general pipeline to apply persistent homology to study time series, particularly the instantaneous heart rate time series for the heart rate variability (HRV) analysis. The first step is capturing the shapes of time series from two different aspects—the persistent homologies and hence persistence diagrams of its sub-level set and Taken's lag map. Second, we propose a systematic and computationally efficient approach to summarize persistence diagrams, which we coined persistence statistics. To demonstrate our proposed method, we apply these tools to the HRV analysis and the sleep-wake, REM-NREM (rapid eyeball movement and non rapid eyeball movement) and sleep-REM-NREM classification problems. The proposed algorithm is evaluated on three different datasets via the cross-database validation scheme. The performance of our approach is better than the state-of-the-art algorithms, and the result is consistent throughout different datasets.

show abstract

Statistical Persistent Homology of Brain Signals

Cited by 20 publications

References 7 publications

Persistent Homology-Based Topological Analysis on the Gestalt Patterns during Human Brain Cognition Process

Persistent Homology-Based Topological Analysis on the Gestalt Patterns during Human Brain Cognition Process

Topological EEG Nonlinear Dynamics Analysis for Emotion Recognition

A Persistent Homology Approach to Heart Rate Variability Analysis With an Application to Sleep-Wake Classification

Contact Info

Product

Resources

About