Phase space reconstruction for improving the classification of single trial EEG
Introduction
Brain–computer interface (BCI) is a system that helps the serious disabled individuals to drive and control external devices using only their brain activity, without participation of peripheral nerves and muscles [1], [2], [3]. The real purpose of BCI is to translate brain activity into a command for a computer. To achieve this goal, the feature extraction and the classification algorithm are employed. More and more evidence indicate that some mental tasks can be recognized from spontaneous EEG signals. Currently, the success in the motor imagery-based BCI can be attributed to the underlying neurophysiological phenomena accompanying motor imagery, termed event-related desynchronization (ERD) and event-related synchronization (ERS) [4]. The μ (8–13 Hz) and β (14–25 Hz) band originating in the sensorimotor cortex have been postulated to be good signal features for EEG-based BCI [5], [6].
Many EEG feature extraction studies have been developed within the recent years. Among these feature extraction methods, autoregressive (AR) models [7], power spectral density (PSD) [8], amplitude–frequency analysis (AFA) [9], wavelet transforms (WT) [10] and other method such as empirical mode decomposition (EMD) [11] technique have been used to process the EEG signals. Rodríguez-Bermúdez et al. presented an efficient Leave-One Out estimation method to choose the most useful features extracted by PSD, Hjorth, AR and WT. Their results showed that the classification results using the proposed method were competitive [8]. Zhang et al. used the amplitude–frequency analysis (AFA) and phase synchronization techniques to realize an online BCI [9]. Xu et al. use fuzzy support vector machine based on the statistical features over the set of the wavelet coefficients to classify the left and right hand motor imagery tasks. The classification results outperformed the winner of the BCI Competition 2003 and 2005 on the same dataset and the same criterion [10]. The EMD approach rests on the identification of signal's nonstationary and nonlinear features which represent different modalities of brain activity captured by the EEG data acquisition system. Park et al. introduced a novel method using extension of the algorithm EMD to determine asymmetry, the liberalization of brain activity [11]. A new set of features including higher-order statistics based on the bispectrum of EEG signals have been applied to the classification of right and left motor imagery for developing EEG-based BCI systems. Zhou et al. stated that by using the bispectrum-based feature extraction, all three classifiers (i.e., linear discriminant analysis (LDA), support vector machine (SVM) classifier, and neural network (NN) classifier) are superior to the winner of the BCI Competition 2003 on the same Graz dataset [12].
From a practical perspective, traditional feature extraction techniques based on AR models and PSD applied to the EEG generally assume that the EEG signals is linear. These methods are insensitive to nonlinear structure contained in a time series. For example, it is well known that given any power spectrum, it is possible to generate a time series with that power spectrum by a linear regressive process. If there is significant nonlinearity in the signal, these methods can miss important information contained in the signal. As the physiological signals such as EEG signals, generally acquired as time series, are often marked by significant nonlinearity that conventional analysis methods often fail to identify [13]. It is more suitable to use nonlinear methods to analyze the EEG signals. Much research such as EMD [11] and the method proposed in reference [12] have tried to overcome this limitation. The simulation results have shown the effectiveness of the nonlinear features. Another popular nonlinear method is phase space reconstruction (PSR), which is a valuable tool for the studies of this kind of signals [14].
A number of authors have looked for the presence of nonlinearity in human EEG signals with varying outcomes. Liley et al. proposed an EEG model to describe the dynamics of neural activity in cortex [15]. Stam analyzed the nonlinear dynamics of EEG and MEG [14]. Many nonlinear features were used to analyze epilepsy, mental fatigue [13], [16], [17]. In the BCI community, only a paucity of research has used the chaotic indices. Banitalebi et al. used largest Lyapunov exponent, mutual information, correlation dimension and minimum embedding dimension as the features for the classification of EEG signals in reference [18]. As it is well known, the calculations of chaos features such as Lyapunov exponent, mutual information etc. is time-consuming. It spend 38.6 s to calculate a maximal Lyapunov exponent index with wolf method for one channel of a trial in MATLAB 7.10(R2010a) running in the machine with 4GB of memory and 3.10 GHz processor. A practical BCI must have a high information transfer rate, so these chaos features such as Lyapunov exponent cannot meet the real-time requirements. To address these deficits, we developed a feature extraction scheme based on PSR. The principle of PSR is to transform the properties of a time series into topological properties of a geometrical object which is embedded in a space, wherein all possible states of the system are represented, each state corresponds to a unique point, and this reconstructed space sharing the same topological properties as the original space [19], [20]. Because the ERD/ERS phenomenon emerges in motor imagery, and the reconstructed attractors are sensitivity to the initial conditions, some useful nonlinear information hidden in the phase space will be revealed. So, all the features extracted in the phase space of the EEG signals must help to improve the classification of the BCI. In the first stage of the proposed scheme, a phase space of the EEG signals is reconstructed. Then the features were extracted in the phase space by AFA. To evaluate the effectiveness of the feature sets, a linear discriminant analysis (LAD) classifier is adopted to classify the Graz BCI datasets which are used in the BCI-Competition 2003 [21] and BCI-Competition 2005 [22]. It should be emphasized that, although the PSR techniques and AFA have been previously analyzed in other BCI research works; this letter introduces a new framework to combine the conventional features extraction methods AFA to chaos theory. To the best knowledge of the authors, this framework has not been previously proposed for implementing BCI systems based on motor imagery.
Section snippets
Data acquisition and description
Two datasets coming from BCI Competition 2003 and 2005 are used in present study. The first dataset is the dataset III of BCI Competition 2003 and the second dataset is the dataset IIIB of BCI Competition 2005. All the two datasets are provided by Department of Medical Informatics, Institute for Biomedical Engineering, University of Technology Graz [21], [22].
In BCI Competition 2003, the dataset III (termed Graz2003 dataset) was recorded over C3, Cz and C4 from a normal subject (female, 25
Amplitude–frequency analysis (AFA)
AFA is a method based on Discrete Fourier transform (DFT). Fourier transform of a sequence x(n) (n = 0, 1, ..., N − 1) with the length of N can obtain a Discrete Fourier transform sequence X(k) (k = 0, 1, …, N − 1) with the length of N. When N can be represented by 2m (m is an integer), the Fourier transform can be calculated by a fast algorithm which is termed Fast Fourier transform (FFT). In generally, it can be expressed as Eq. (1):
takes the absolute
Results and discussions
The benchmark EEG datasets which were used in the BCI-Competition 2003 and 2005 are used to verify the effectiveness of the proposed scheme. All simulations have been carried out in MATLAB 7.10(R2010a) environment running in the same machine with 4 GB of memory and 3.10 GHz processor. For Graz2003 dataset, only the sliding windows from t = 3 to t = 9 s were used according to the time scheme of the 2003 experimental paradigm [21]. The classification accuracy is the most commonly used evaluation
Conclusion
This work presents a feature extraction method to extract features in phase space for classifying EEG signals corresponding to left/right-hand motor imagery. The features were extracted in phase space using AFA method. The peak values and mean values of μ and β band are used as the features. Experimental results have shown that based on the proposed features, the LDA classifier achieve better classification performance than the traditional features extracted by AFA in original EEG signals.
Acknowledgments
This work is sponsored by “National 111” Project of China (B08036) and the Fundamental Research Funds for the Central Universities (No. XDJK2010C025).
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