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Kumari A, Edla DR, Reddy RR, Jannu S, Vidyarthi A, Alkhayyat A, de Marin MSG. EEG-based motor imagery channel selection and classification using hybrid optimization and two-tier deep learning. J Neurosci Methods 2024; 409:110215. [PMID: 38968976 DOI: 10.1016/j.jneumeth.2024.110215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2024] [Revised: 06/14/2024] [Accepted: 06/28/2024] [Indexed: 07/07/2024]
Abstract
Brain-computer interface (BCI) technology holds promise for individuals with profound motor impairments, offering the potential for communication and control. Motor imagery (MI)-based BCI systems are particularly relevant in this context. Despite their potential, achieving accurate and robust classification of MI tasks using electroencephalography (EEG) data remains a significant challenge. In this paper, we employed the Minimum Redundancy Maximum Relevance (MRMR) algorithm to optimize channel selection. Furthermore, we introduced a hybrid optimization approach that combines the War Strategy Optimization (WSO) and Chimp Optimization Algorithm (ChOA). This hybridization significantly enhances the classification model's overall performance and adaptability. A two-tier deep learning architecture is proposed for classification, consisting of a Convolutional Neural Network (CNN) and a modified Deep Neural Network (M-DNN). The CNN focuses on capturing temporal correlations within EEG data, while the M-DNN is designed to extract high-level spatial characteristics from selected EEG channels. Integrating optimal channel selection, hybrid optimization, and the two-tier deep learning methodology in our BCI framework presents an enhanced approach for precise and effective BCI control. Our model got 95.06% accuracy with high precision. This advancement has the potential to significantly impact neurorehabilitation and assistive technology applications, facilitating improved communication and control for individuals with motor impairments.
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Affiliation(s)
- Annu Kumari
- Department of Computer Science and Engineering, National Institute of Technology Goa, Cuncolim, South Goa, 403 703, Goa, India.
| | - Damodar Reddy Edla
- Department of Computer Science and Engineering, National Institute of Technology Goa, Cuncolim, South Goa, 403 703, Goa, India.
| | - R Ravinder Reddy
- Department of Computer Science and Engineering, Chaitanya Bharathi Institute of Technology, Hyderabad, 500 075, India.
| | - Srikanth Jannu
- Department of Computer Science and Engineering, Vaagdevi Engineering College, Warangal, Telangana, 506 005, India.
| | - Ankit Vidyarthi
- Department of CSE&IT, Jaypee Institute of Information Technology, Noida, Uttar Pradesh, 201309, India.
| | | | - Mirtha Silvana Garat de Marin
- Engineering Research & Innovation Group, Universidad Europea del Atlántico, C/Isabel Torres 21, 39011 Santander, Spain; Department of Project Management, Universidad Internacional Iberoamericana, Arecibo, PR 00613, USA; Department of Project Management, Universidade Internacional do Cuanza, Estrada Nacional 250, Bairro Kaluapanda, Cuito-Bié, Angola.
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Abenna S, Nahid M, Bouyghf H, Ouacha B. An enhanced motor imagery EEG signals prediction system in real-time based on delta rhythm. Biomed Signal Process Control 2023. [DOI: 10.1016/j.bspc.2022.104210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Wang G, Cerf M. Brain-Computer Interface using neural network and temporal-spectral features. Front Neuroinform 2022; 16:952474. [PMID: 36277476 PMCID: PMC9580359 DOI: 10.3389/fninf.2022.952474] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2022] [Accepted: 08/24/2022] [Indexed: 11/24/2022] Open
Abstract
Brain-Computer Interfaces (BCIs) are increasingly useful for control. Such BCIs can be used to assist individuals who lost mobility or control over their limbs, for recreational purposes such as gaming or semi-autonomous driving, or as an interface toward man-machine integration. Thus far, the performance of algorithms used for thought decoding has been limited. We show that by extracting temporal and spectral features from electroencephalography (EEG) signals and, following, using deep learning neural network to classify those features, one can significantly improve the performance of BCIs in predicting which motor action was imagined by a subject. Our movement prediction algorithm uses Sequential Backward Selection technique to jointly choose temporal and spectral features and a radial basis function neural network for the classification. The method shows an average performance increase of 3.50% compared to state-of-the-art benchmark algorithms. Using two popular public datasets our algorithm reaches 90.08% accuracy (compared to an average benchmark of 79.99%) on the first dataset and 88.74% (average benchmark: 82.01%) on the second dataset. Given the high variability within- and across-subjects in EEG-based action decoding, we suggest that using features from multiple modalities along with neural network classification protocol is likely to increase the performance of BCIs across various tasks.
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Affiliation(s)
- Gan Wang
- School of Mechanical and Electrical Engineering, Soochow University, Suchow, China
| | - Moran Cerf
- Interdepartmental Neuroscience Program, Northwestern University, Evanston, IL, United States
- *Correspondence: Moran Cerf,
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A novel multi-branch hybrid neural network for motor imagery EEG signal classification. Biomed Signal Process Control 2022. [DOI: 10.1016/j.bspc.2022.103718] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Arpaia P, Esposito A, Natalizio A, Parvis M. How to successfully classify EEG in motor imagery BCI: a metrological analysis of the state of the art. J Neural Eng 2022; 19. [PMID: 35640554 DOI: 10.1088/1741-2552/ac74e0] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2021] [Accepted: 05/31/2022] [Indexed: 11/11/2022]
Abstract
Objective. Processing strategies are analysed with respect to the classification of electroencephalographic signals related to brain-computer interfaces based on motor imagery. A review of literature is carried out to understand the achievements in motor imagery classification, the most promising trends, and the challenges in replicating these results. Main focus is placed on performance by means of a rigorous metrological analysis carried out in compliance with the international vocabulary of metrology. Hence, classification accuracy and its uncertainty are considered, as well as repeatability and reproducibility.Approach. The paper works included in the review concern the classification of electroencephalographic signals in motor-imagery- based brain-computer interfaces. Article search was carried out in accordance with the PRISMA standard and 89 studies were included.Main results. Statistically-based analyses show that brain-inspired approaches are increasingly proposed, and that these are particularly successful in discriminating against multiple classes. Notably, many proposals involve convolutional neural networks. Instead, classical machine learning approaches are still effective for binary classifications. Many proposals combine common spatial pattern, least absolute shrinkage and selection operator, and support vector machines. Regarding reported classification accuracies, performance above the upper quartile is in the 85 % to 100 % range for the binary case and in the 83 % to 93 % range for multi-class one. Associated uncertainties are up to 6 % while repeatability for a predetermined dataset is up to 8 %. Reproducibility assessment was instead prevented by lack of standardization in experiments.Significance. By relying on the analysed studies, the reader is guided towards the development of a successful processing strategy as a crucial part of a brain-computer interface. Moreover, it is suggested that future studies should extend these approaches on data from more subjects and with custom experiments, even by investigating online operation. This would also enable the quantification of results reproducibility.
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Affiliation(s)
- Pasquale Arpaia
- Centro Interdipartimentale di Ricerca in Management Sanitario e Innovazione in Sanità, Università degli Studi di Napoli Federico II, Via Claudio, 21, Napoli, Campania, 80125, ITALY
| | - Antonio Esposito
- Department of Electronics and Telecommunications (DET), Politecnico di Torino, Corso Castelfidardo, 39, Torino, 10129, ITALY
| | - Angela Natalizio
- Department of Electronics and Telecommunications (DET), Politecnico di Torino, Corso Castelfidardo, 39, Torino, Piemonte, 10129, ITALY
| | - Marco Parvis
- Department of Electronics and Telecommunications (DET), Politecnico di Torino, Corso Castelfidardo, 39, Torino, Piemonte, 10129, ITALY
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Radman M, Chaibakhsh A, Nariman-zadeh N, He H. Feature fusion for improving performance of motor imagery brain-computer interface system. Biomed Signal Process Control 2021. [DOI: 10.1016/j.bspc.2021.102763] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Dagdevir E, Tokmakci M. Optimization of preprocessing stage in EEG based BCI systems in terms of accuracy and timing cost. Biomed Signal Process Control 2021. [DOI: 10.1016/j.bspc.2021.102548] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Yang L, Song Y, Ma K, Xie L. Motor Imagery EEG Decoding Method Based on a Discriminative Feature Learning Strategy. IEEE Trans Neural Syst Rehabil Eng 2021; 29:368-379. [PMID: 33460382 DOI: 10.1109/tnsre.2021.3051958] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
With the rapid development of deep learning, more and more deep learning-based motor imagery electroencephalograph (EEG) decoding methods have emerged in recent years. However, the existing deep learning-based methods usually only adopt the constraint of classification loss, which hardly obtains the features with high discrimination and limits the improvement of EEG decoding accuracy. In this paper, a discriminative feature learning strategy is proposed to improve the discrimination of features, which includes the central distance loss (CD-loss), the central vector shift strategy, and the central vector update process. First, the CD-loss is proposed to make the same class of samples converge to the corresponding central vector. Then, the central vector shift strategy extends the distance between different classes of samples in the feature space. Finally, the central vector update process is adopted to avoid the non-convergence of CD-loss and weaken the influence of the initial value of central vectors on the final results. In addition, overfitting is another severe challenge for deep learning-based EEG decoding methods. To deal with this problem, a data augmentation method based on circular translation strategy is proposed to expand the experimental datasets without introducing any extra noise or losing any information of the original data. To validate the effectiveness of the proposed method, we conduct some experiments on two public motor imagery EEG datasets (BCI competition IV 2a and 2b dataset), respectively. The comparison with current state-of-the-art methods indicates that our method achieves the highest average accuracy and good stability on the two experimental datasets.
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Yang L, Song Y, Ma K, Su E, Xie L. A novel motor imagery EEG decoding method based on feature separation. J Neural Eng 2021; 18. [PMID: 33545691 DOI: 10.1088/1741-2552/abe39b] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2020] [Accepted: 02/05/2021] [Indexed: 11/11/2022]
Abstract
OBJECTIVE Motor imagery electroencephalography (EEG) decoding is a vital technology for the brain-computer interface (BCI) systems and has been widely studied in recent years. However, the original EEG signals usually contain a lot of class-independent information, and the existing motor imagery EEG decoding methods are easily interfered by this irrelevant information, which greatly limits the decoding accuracy of these methods. APPROACH To overcome the interference of the class-independent information, a motor imagery EEG decoding method based on feature separation is proposed in this paper. Furthermore, a feature separation network based on adversarial learning (FSNAL) is designed for the feature separation of the original EEG samples. First, the class-related features and class-independent features are separated by the proposed FSNAL framework, and then motor imagery EEG decoding is performed only according to the class-related features to avoid the adverse effects of class-independent features. MAIN RESULTS To validate the effectiveness of the proposed motor imagery EEG decoding method, we conduct some experiments on two public EEG datasets (the BCI competition IV 2a and 2b datasets). The experimental results comparison between our method and some state-of-the-art methods demonstrates that our motor imagery EEG decoding method outperforms all the compared methods on the two experimental datasets. SIGNIFICANCE Our motor imagery EEG decoding method can alleviate the interference of class-independent features, and it has great application potential for improving the performance of motor imagery BCI systems in the near future.
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Affiliation(s)
- Lie Yang
- Shien-Ming Wu School of Intelligent Engineering, South China University of Technology, No.777 East Xingye Avenue, Panyu District, Guangzhou, Guangzhou, 510460, CHINA
| | - Yonghao Song
- Shien-Ming Wu School of Intelligent Engineering, South China University of Technology, No.777 East Xingye Avenue, Panyu District, Guangzhou, Guangzhou, Guangdong, 510460, CHINA
| | - Ke Ma
- Sun Yat-Sen University Zhongshan Ophthalmic Center State Key Laboratory of Ophthalmology, No.54 Xianlie South Road, Yuexiu District, Guangzhou, Guangzhou, Guangdong, 510000, CHINA
| | - Enze Su
- Shien-Ming Wu School of Intelligent Engineering, South China University of Technology, No.777 East Xingye Avenue, Panyu District, Guangzhou, Guangzhou, Guangdong, 510460, CHINA
| | - Longhan Xie
- Shien-Ming Wu School of Intelligent Engineering, South China University of Technology, No.777 East Xingye Avenue, Panyu District, Guangzhou, Guangzhou, Guangdong, 510460, CHINA
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Shamsi F, Haddad A, Najafizadeh L. Early classification of motor tasks using dynamic functional connectivity graphs from EEG. J Neural Eng 2020; 18. [PMID: 33246319 DOI: 10.1088/1741-2552/abce70] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Accepted: 11/27/2020] [Indexed: 12/13/2022]
Abstract
OBJECTIVE Classification of electroencephalography (EEG) signals with high accuracy using short recording intervals has been a challenging problem in developing brain computer interfaces (BCIs). This paper presents a novel feature extraction method for EEG recordings to tackle this problem. APPROACH The proposed approach is based on the concept that the brain functions in a dynamic manner, and utilizes dynamic functional connectivity graphs. The EEG data is first segmented into intervals during which functional networks sustain their connectivity. Functional connectivity networks for each identified segment are then localized, and graphs are constructed, which will be used as features. To take advantage of the dynamic nature of the generated graphs, a Long Short Term Memory (LSTM) classifier is employed for classification. MAIN RESULTS Features extracted from various durations of post-stimulus EEG data associated with motor execution and imagery tasks are used to test the performance of the classifier. Results show an average accuracy of 85.32% using features extracted from only 500 ms of the post-stimulus data. SIGNIFICANCE Our results demonstrate, for the first time, that using the proposed feature extraction method, it is possible to classify motor tasks from EEG recordings using a short interval of the data in the order of hundreds of milliseconds (e.g. 500 ms). This duration is considerably shorter than what has been reported before. These results will have significant implications for improving the effectiveness and the speed of BCIs, particularly for those used in assistive technologies.
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Affiliation(s)
- Foroogh Shamsi
- Electrical and Computer Engineering, Rutgers University, 94 Brett Rd, New Brunswick, New Jersey, NJ 08854, UNITED STATES
| | - Ali Haddad
- Electrical and Computer Engineering, Rutgers University, 94 Brett Rd, New Brunswick, New Jersey, NJ 08854, UNITED STATES
| | - Laleh Najafizadeh
- Electrical and Computer Engineering, Rutgers University, 94 Brett Rd, New Brunswick, New Jersey, 08901-8554, UNITED STATES
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Feng N, Hu F, Wang H, Gouda MA. Decoding of voluntary and involuntary upper-limb motor imagery based on graph fourier transform and cross-frequency coupling coefficients. J Neural Eng 2020; 17:056043. [PMID: 33045685 DOI: 10.1088/1741-2552/abc024] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
OBJECTIVE Brain-computer interface (BCI) technology based on motor imagery (MI) control has become a research hotspot but continues to encounter numerous challenges. BCI can assist in the recovery of stroke patients and serve as a key technology in robot control. Current research on MI almost exclusively focuses on the hands, feet, and tongue. Therefore, the purpose of this paper is to establish a four-class MI BCI system, in which the four types are the four articulations within the right upper limbs, involving the shoulder, elbow, wrist, and hand. APPROACH Ten subjects were chosen to perform nine upper-limb analytic movements, after which the differences were compared in P300, movement-related potentials(MRPS), and event-related desynchronization/event-related synchronization under voluntary MI (V-MI) and involuntary MI (INV-MI). Next, the cross-frequency coupling (CFC) coefficient based on mutual information was extracted from the electrodes and frequency bands with interest. Combined with the image Fourier transform and twin bounded support vector machine classifier, four kinds of electroencephalography data were classified, and the classifier's parameters were optimized using a genetic algorithm. MAIN RESULTS The results were shown to be encouraging, with an average accuracy of 93.2% and 92.2% for V-MI and INV-MI, respectively, and over 95% for any three classes and any two classes. In most cases, the accuracy of feature extraction using the proximal articulations as the basis was found to be relatively high and had better performance. SIGNIFICANCE This paper discussed four types of MI according to three aspects under two modes and classed them by combining graph Fourier transform and CFC. Accordingly, the theoretical discussion and classification methods may provide a fundamental theoretical basis for BCI interface applications.
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Affiliation(s)
- Naishi Feng
- Department of Mechanical Engineering and Automation, Northeastern University, Shenyang City, Liaoning, People's Republic of China
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Luo J, Gao X, Zhu X, Wang B, Lu N, Wang J. Motor imagery EEG classification based on ensemble support vector learning. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2020; 193:105464. [PMID: 32283387 DOI: 10.1016/j.cmpb.2020.105464] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2019] [Revised: 02/27/2020] [Accepted: 03/18/2020] [Indexed: 06/11/2023]
Abstract
BACKGROUND AND OBJECTIVE Brain-computer interfaces build a communication pathway from the human brain to a computer. Motor imagery-based electroencephalogram (EEG) classification is a widely applied paradigm in brain-computer interfaces. The common spatial pattern, based on the event-related desynchronization (ERD)/event-related synchronization (ERS) phenomenon, is one of the most popular algorithms for motor imagery-based EEG classification. Moreover, the spatiotemporal discrepancy feature based on the event-related potential phenomenon has been demonstrated to provide complementary information to ERD/ERS-based features. In this paper, aiming to improve the performance of motor imagery-based EEG classification in a few-channel situation, an ensemble support vector learning (ESVL)-based approach is proposed to combine the advantages of the ERD/ERS-based features and the event-related potential-based features in motor imagery-based EEG classification. METHODS ESVL is an ensemble learning algorithm based on support vector machine classifier. Specifically, the decision boundary with the largest interclass margin is obtained using the support vector machine algorithm, and the distances between sample points and the decision boundary are mapped to posterior probabilities. The probabilities obtained from different support vector machine classifiers are combined to make prediction. Thus, ESVL leverages the advantages of multiple trained support vector machine classifiers and makes a better prediction based on the posterior probabilities. The class discrepancy-guided sub-band-based common spatial pattern and the spatiotemporal discrepancy feature are applied to extract discriminative features, and then, the extracted features are used to train the ESVL classifier and make predictions. RESULTS The BCI Competition IV datasets 2a and 2b are employed to evaluate the performance of the proposed ESVL algorithm. Experimental comparisons with the state-of-the-art methods are performed, and the proposed ESVL-based approach achieves an average max kappa value of 0.60 and 0.71 on BCI Competition IV datasets 2a and 2b respectively. The results show that the proposed ESVL-based approach improves the performance of motor imagery-based brain-computer interfaces. CONCLUSION The proposed ESVL classifier could use the posterior probabilities to realize ensemble learning and the ESVL-based motor imagery classification approach takes advantage of the merits of ERD/ERS based feature and event-related potential based feature to improve the experimental performance.
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Affiliation(s)
- Jing Luo
- Shaanxi Key Laboratory for Network Computing and Security Technology, School of Computer Science and Engineering, Xi'an University of Technology, Xi'an Shaanxi, China.
| | - Xing Gao
- Shaanxi Key Laboratory for Network Computing and Security Technology, School of Computer Science and Engineering, Xi'an University of Technology, Xi'an Shaanxi, China
| | - Xiaobei Zhu
- Shaanxi Key Laboratory for Network Computing and Security Technology, School of Computer Science and Engineering, Xi'an University of Technology, Xi'an Shaanxi, China
| | - Bin Wang
- Shaanxi Key Laboratory for Network Computing and Security Technology, School of Computer Science and Engineering, Xi'an University of Technology, Xi'an Shaanxi, China
| | - Na Lu
- State Key Laboratory for Manufacturing Systems Engineering, Systems Engineering Institute, Xi'an Jiaotong University, Xi'an, Shaanxi, China
| | - Jie Wang
- State Key Laboratory for Manufacturing Systems Engineering, Systems Engineering Institute, Xi'an Jiaotong University, Xi'an, Shaanxi, China
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An adaptive multi-domain feature joint optimization framework based on composite kernels and ant colony optimization for motor imagery EEG classification. Biomed Signal Process Control 2020. [DOI: 10.1016/j.bspc.2020.101994] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Singh A, Lal S, Guesgen HW. Reduce Calibration Time in Motor Imagery Using Spatially Regularized Symmetric Positives-Definite Matrices Based Classification. SENSORS (BASEL, SWITZERLAND) 2019; 19:E379. [PMID: 30658523 PMCID: PMC6359529 DOI: 10.3390/s19020379] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Revised: 12/28/2018] [Accepted: 01/14/2019] [Indexed: 11/30/2022]
Abstract
Electroencephalogram (EEG) based motor imagery brain⁻computer interface (BCI) requires large number of subject specific training trials to calibrate the system for a new subject. This results in long calibration time that limits the BCI usage in practice. One major challenge in the development of a brain⁻computer interface is to reduce calibration time or completely eliminate it. To address this problem, existing approaches use covariance matrices of electroencephalography (EEG) trials as descriptors for decoding BCI but do not consider the geometry of the covariance matrices, which lies in the space of Symmetric Positive Definite (SPD) matrices. This inevitably limits their performance. We focus on reducing calibration time by introducing SPD based classification approach. However, SPD-based classification has limited applicability in small training sets because the dimensionality of covariance matrices is large in proportion to the number of trials. To overcome this drawback, our paper proposes a new framework that transforms SPD matrices in lower dimension through spatial filter regularized by prior information of EEG channels. The efficacy of the proposed approach was validated on the small sample scenario through Dataset IVa from BCI Competition III. The proposed approach achieved mean accuracy of 86.13 % and mean kappa of 0.72 on Dataset IVa. The proposed method outperformed other approaches in existing studies on Dataset IVa. Finally, to ensure the robustness of the proposed method, we evaluated it on Dataset IIIa from BCI Competition III and Dataset IIa from BCI Competition IV. The proposed method achieved mean accuracy 92.22 % and 81.21 % on Dataset IIIa and Dataset IIa, respectively.
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Affiliation(s)
- Amardeep Singh
- School of Fundamental Sciences, Massey University, Manawatu Private Bag 11 222, Palmerston North 4442, New Zealand.
| | - Sunil Lal
- School of Fundamental Sciences, Massey University, Manawatu Private Bag 11 222, Palmerston North 4442, New Zealand.
| | - Hans W Guesgen
- School of Fundamental Sciences, Massey University, Manawatu Private Bag 11 222, Palmerston North 4442, New Zealand.
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