1
|
Gancio J, Masoller C, Tirabassi G. Permutation entropy analysis of EEG signals for distinguishing eyes-open and eyes-closed brain states: Comparison of different approaches. CHAOS (WOODBURY, N.Y.) 2024; 34:043130. [PMID: 38598676 DOI: 10.1063/5.0200029] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2024] [Accepted: 03/27/2024] [Indexed: 04/12/2024]
Abstract
Developing reliable methodologies to decode brain state information from electroencephalogram (EEG) signals is an open challenge, crucial to implementing EEG-based brain-computer interfaces (BCIs). For example, signal processing methods that identify brain states could allow motor-impaired patients to communicate via non-invasive, EEG-based BCIs. In this work, we focus on the problem of distinguishing between the states of eyes closed (EC) and eyes open (EO), employing quantities based on permutation entropy (PE). An advantage of PE analysis is that it uses symbols (ordinal patterns) defined by the ordering of the data points (disregarding the actual values), hence providing robustness to noise and outliers due to motion artifacts. However, we show that for the analysis of multichannel EEG recordings, the performance of PE in discriminating the EO and EC states depends on the symbols' definition and how their probabilities are estimated. Here, we study the performance of PE-based features for EC/EO state classification in a dataset of N=107 subjects with one-minute 64-channel EEG recordings in each state. We analyze features obtained from patterns encoding temporal or spatial information, and we compare different approaches to estimate their probabilities (by averaging over time, over channels, or by "pooling"). We find that some PE-based features provide about 75% classification accuracy, comparable to the performance of features extracted with other statistical analysis techniques. Our work highlights the limitations of PE methods in distinguishing the eyes' state, but, at the same time, it points to the possibility that subject-specific training could overcome these limitations.
Collapse
Affiliation(s)
- Juan Gancio
- Universitat Politècnica de Catalunya, Departament de Fisica, Rambla Sant Nebridi 22, Terrassa, Barcelona 08222, Spain
| | - Cristina Masoller
- Universitat Politècnica de Catalunya, Departament de Fisica, Rambla Sant Nebridi 22, Terrassa, Barcelona 08222, Spain
| | - Giulio Tirabassi
- Universitat Politècnica de Catalunya, Departament de Fisica, Rambla Sant Nebridi 22, Terrassa, Barcelona 08222, Spain
- Universitat de Girona, Departament de Informàtica, Matemàtica Aplicada i Estadística, Universitat de Girona, Carrer de la Universitat de Girona 6, Girona 17003, Spain
| |
Collapse
|
2
|
Bröhl T, Rings T, Pukropski J, von Wrede R, Lehnertz K. The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives. FRONTIERS IN NETWORK PHYSIOLOGY 2024; 3:1338864. [PMID: 38293249 PMCID: PMC10825060 DOI: 10.3389/fnetp.2023.1338864] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/15/2023] [Accepted: 12/19/2023] [Indexed: 02/01/2024]
Abstract
Epilepsy is now considered a network disease that affects the brain across multiple levels of spatial and temporal scales. The paradigm shift from an epileptic focus-a discrete cortical area from which seizures originate-to a widespread epileptic network-spanning lobes and hemispheres-considerably advanced our understanding of epilepsy and continues to influence both research and clinical treatment of this multi-faceted high-impact neurological disorder. The epileptic network, however, is not static but evolves in time which requires novel approaches for an in-depth characterization. In this review, we discuss conceptual basics of network theory and critically examine state-of-the-art recording techniques and analysis tools used to assess and characterize a time-evolving human epileptic brain network. We give an account on current shortcomings and highlight potential developments towards an improved clinical management of epilepsy.
Collapse
Affiliation(s)
- Timo Bröhl
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - Thorsten Rings
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - Jan Pukropski
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
| | - Randi von Wrede
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
- Interdisciplinary Center for Complex Systems, University of Bonn, Bonn, Germany
| |
Collapse
|
3
|
Zunino L, Soriano MC. Quantifying the diversity of multiple time series with an ordinal symbolic approach. Phys Rev E 2023; 108:065302. [PMID: 38243479 DOI: 10.1103/physreve.108.065302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2023] [Accepted: 11/13/2023] [Indexed: 01/21/2024]
Abstract
The main motivation of this paper is to introduce the ordinal diversity, a symbolic tool able to quantify the degree of diversity of multiple time series. Analytical, numerical, and experimental analyses illustrate the utility of this measure to quantify how diverse, from an ordinal perspective, a set of many time series is. We have shown that ordinal diversity is able to characterize dynamical richness and dynamical transitions in stochastic processes and deterministic systems, including chaotic regimes. This ordinal tool also serves to identify optimal operating conditions in the machine learning approach of reservoir computing. These results allow us to envision potential applications for the handling and characterization of large amounts of data, paving the way for addressing some of the most pressing issues facing the current big data paradigm.
Collapse
Affiliation(s)
- Luciano Zunino
- Centro de Investigaciones Ópticas (CONICET La Plata - CIC - UNLP), C.C. 3, 1897 Gonnet, La Plata, Argentina
- Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata, Argentina
| | - Miguel C Soriano
- Instituto de Física Interdisciplinar y Sistemas Complejos CSIC-UIB, Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| |
Collapse
|
4
|
Almendral JA, Leyva I, Sendiña-Nadal I. Unveiling the Connectivity of Complex Networks Using Ordinal Transition Methods. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1079. [PMID: 37510026 PMCID: PMC10378875 DOI: 10.3390/e25071079] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Revised: 07/10/2023] [Accepted: 07/14/2023] [Indexed: 07/30/2023]
Abstract
Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand information interchange in the networks of dynamical systems, and uncover the interplay between dynamics and structure during the synchronization process, remains relatively unexplored. Here, we compare the ordinal permutation entropy, a standard complexity measure in the literature, and the permutation entropy of the ordinal transition probability matrix that describes the transitions between the ordinal patterns derived from a time series. We find that the permutation entropy based on the ordinal transition matrix outperforms the rest of the tested measures in discriminating the topological role of networked chaotic Rössler systems. Since the method is based on permutation entropy measures, it can be applied to arbitrary real-world time series exhibiting correlations originating from an existing underlying unknown network structure. In particular, we show the effectiveness of our method using experimental datasets of networks of nonlinear oscillators.
Collapse
Affiliation(s)
- Juan A Almendral
- Complex Systems Group & Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
- Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - I Leyva
- Complex Systems Group & Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
- Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - Irene Sendiña-Nadal
- Complex Systems Group & Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
- Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain
| |
Collapse
|
5
|
Kottlarz I, Parlitz U. Ordinal pattern-based complexity analysis of high-dimensional chaotic time series. CHAOS (WOODBURY, N.Y.) 2023; 33:2888089. [PMID: 37133925 DOI: 10.1063/5.0147219] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 04/04/2023] [Indexed: 05/04/2023]
Abstract
The ordinal pattern-based complexity-entropy plane is a popular tool in nonlinear dynamics for distinguishing stochastic signals (noise) from deterministic chaos. Its performance, however, has mainly been demonstrated for time series from low-dimensional discrete or continuous dynamical systems. In order to evaluate the usefulness and power of the complexity-entropy (CE) plane approach for data representing high-dimensional chaotic dynamics, we applied this method to time series generated by the Lorenz-96 system, the generalized Hénon map, the Mackey-Glass equation, the Kuramoto-Sivashinsky equation, and to phase-randomized surrogates of these data. We find that both the high-dimensional deterministic time series and the stochastic surrogate data may be located in the same region of the complexity-entropy plane, and their representations show very similar behavior with varying lag and pattern lengths. Therefore, the classification of these data by means of their position in the CE plane can be challenging or even misleading, while surrogate data tests based on (entropy, complexity) yield significant results in most cases.
Collapse
Affiliation(s)
- Inga Kottlarz
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
- Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
- Department of Pharmacology and Toxicology, University Medical Center Göttingen (UMG), Robert-Koch-Str. 40, 37075 Göttingen, Germany
- German Center for Cardiovascular Research (DZHK), partner site Göttingen, Robert-Koch-Str. 42a, 37075 Göttingen, Germany
| | - Ulrich Parlitz
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
- Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
- German Center for Cardiovascular Research (DZHK), partner site Göttingen, Robert-Koch-Str. 42a, 37075 Göttingen, Germany
| |
Collapse
|
6
|
Hirata Y, Amigó JM. A review of symbolic dynamics and symbolic reconstruction of dynamical systems. CHAOS (WOODBURY, N.Y.) 2023; 33:2887746. [PMID: 37125938 DOI: 10.1063/5.0146022] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2023] [Accepted: 04/08/2023] [Indexed: 05/03/2023]
Abstract
Discretizing a nonlinear time series enables us to calculate its statistics fast and rigorously. Before the turn of the century, the approach using partitions was dominant. In the last two decades, discretization via permutations has been developed to a powerful methodology, while recurrence plots have recently begun to be recognized as a method of discretization. In the meantime, horizontal visibility graphs have also been proposed to discretize time series. In this review, we summarize these methods and compare them from the viewpoint of symbolic dynamics, which is the right framework to study the symbolic representation of nonlinear time series and the inverse process: the symbolic reconstruction of dynamical systems. As we will show, symbolic dynamics is currently a very active research field with interesting applications.
Collapse
Affiliation(s)
- Yoshito Hirata
- Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - José M Amigó
- Centro de Investigación Operativa, Universidad Miguel Hernández, 03202 Elche, Spain
| |
Collapse
|