A sequential method using multiplicative extreme learning machine for epileptic seizure detection

Abstract

Epilepsy, one of the most common neurological disorders of the human brain, is unpredictable and irregular. There is much difficulty involved in its detection. Here, a sequential processing feature extraction method and a novel multiplicative extreme learning machine are proposed for using in the electroencephalogram (EEG) classification process towards epileptic seizure detection. Firstly, a discrete wavelet transform (DWT) algorithm based on the frequency decomposition is used to obtain the sub-band wavelet coefficients. Secondly, two-dimensional (2D) and three-dimensional (3D) phase space reconstruction (PSR) of the sub-band are calculated to reveal the nonlinear chaos characteristics of signals in the high dimension. Thirdly, and differing from other statistical methods, the singular values are calculated based on the covariance matrix of 2D or 3D phase space as features that reduce the correlation of each dimension and which demonstrate the crucial variance in the original EEG signals. A combination of the proposed sequential methods can extract the significant features of epileptic seizure signals for classification. Finally, a novel multiplicative extreme learning machine (M-ELM) is proposed for using in the classification process. As compared with the normal ELM, support vector machine (SVM) with different kernels and backpropagation (BP) neural networks, the use of M-ELM can further improve the classification accuracy rate of the seizure signals, seizure free signals and healthy signals from the public dataset. Tests of the proposed epilepsy detection approach can achieve the highest 100% detection accuracy with rapid calculation speed.

Introduction

Epilepsy is one of the most common neurological disorders. It is associated with the high level of activity of nerve cells and effects over 1% of the world's population. It is unpredictable and the associated recurrent seizures feature makes it very difficult to deal with [1].

The development of electroencephalography (EEG) over the last few decades has provided an effective technique to assess brain activity and related disorders through the cerebral cortex with non-invasive and low-cost in clinical trials [2]. At the commencement of epilepsy seizures, a small number of brain cells begin weakly discharge. This usually occurs at a level below the awareness of patient. The characteristic EEG signals of epilepsy seizure often display spike waves and sharp waves. For the clinical diagnosis epilepsy seizures, doctors and neurologists usually rely on their own experiences and visual EEG signal inspection to interpret such patterns. However, visual inspection by an EEG expert for discriminating long-term EEGs record is quite time-consuming. Epileptic seizures’ prediction is still challenging because of the limited macroscopic information currently available relating to the specific nature and patterns of the associated EEG signals. An effective method for automatic seizure detection of seizure and non-seizure EEG segments would be desirable to help the clinician give a proper diagnosis and formulate a possible treatment plan for epilepsy. There are two major aspects in the field of EEG analysis, namely feature extraction and classification.

A considerable number of feature extraction methods have now been developed for detection of EEG signals. The main aspects of these are time domain analysis, frequency domain analysis, time–frequency domain analysis and the nonlinear dynamic method [3], [4], [5], [6]. Autoregressive (AR) models, based on frequency domain techniques use the combination of time series and the estimated parameter. Amplitude-frequency analysis (AFA) is based on the Discrete Fourier transformation. Both of these reveal the mechanism of epilepsy seizure signals [7], [8]. However, both AFA and AR models assume linearity, Gaussianality and minimum-phase within EEG signals. In this way the nonlinear features in the EEG are neglected [9]. Due to the uncertainty of time domain or frequency domain resolution, techniques based on time–frequency domain are used for analyzing the non-stationary EEG signals with spike waves, spark waves and spike and slow waves, among which discrete wavelet transformation (DWT) is very common leading to the extraction feature [10], [11], [12], [13]. Due to its scalable factor, DWT performs well in locating the spike features and transient information in epilepsy EEG signals. Moreover, DWT shows good inhibition towards the artifacts of EEG signals. After the wavelet processing, the EEG data provides a stronger outcome than that of the clinician simply and directly analyzing the original data.

From the view of nonlinearity, due to the frequent signal distortion in the transmission process in the brain's cerebral cortex, the EEG time series have often high dimensionality and displays chaotic behavior. It is very difficult for experts to elucidate the internal mechanism of such signals. Therefore, a lot of nonlinear dynamics tools are used in the feature extraction process. These include the Lyapunov exponent, based on the technique of state space reconstruction with delay coordinates [14], [15], and correlation dimension, which is used to measure the complexity or degree of the EEG signal disorder and synchronization [15]. Other entropy-based nonlinear features are extracted using the approximate entropy (ApEn), permutation entropy (PE) and sample entropy (SampEn) of EEG signals [16], [17]. Recently, the phase space reconstruction (PSR) method has been widely used by researchers to extend EEG sequence signals to 2D or to a higher dimension to reveal the hidden information of signals. Compared with other nonlinear signal analysis methods, such as the Lyapunov exponent and correlation dimension calculation of chaos features, the PSR method is time-saving and can meet real time application requirements. Lee plotted the phase-space reconstruction in a two-dimensional phase space diagram and calculated the Euclidean distance for the process of feature extraction of EEG signals [18]. Chen et al. used the AFA to extract the phase space features (PSF) in the state space of EEG signals [9]. Rajeev et al. used 95% confidence ellipse area for 2D PSR and the interquartile range (IQR) of the Euclidian distances for 3D PSR of IMFs as epilepsy EEG signals features [19].

After feature selection, artificial neural network, such as multilayer perceptron neural networks (MLPNNs) [10], recurrent neural networks (RNNs) [14] and adaptive neuro-fuzzy inference system (ANFIS) [20] can be used in the signal classification process. In particular, feedforward neural networks such as the support vector machine (SVM) based on maximum margin hyperplane in the projection space and backpropagation neural networks (BP NNs) based on dynamic gradient are used to deliver excellent performances in prediction and classification of EEG signals [11], [21], [22]. Kai et al. used SVM with radial basis function (RBF) kernel to identify the feature obtained from Hilbert–Huang transform (HHT) [23]. The feature space obtained from the ellipse area parameters of two IMFs has been used as inputs to the artificial BP NNs classifier [19]. However, these methods have some criticisms on their slow learning speed and parameters adjustment problems. Recently, the extreme learning machine (ELM) as proposed by Huang et al. shows great advantages [24], [25] and can be used to cope with such problems. Its simplified neural network structure increases the learning speed and has been successfully applied to the classification of EEG signals [2], [26]. In order to enhance the nonlinearity of the Universal Learning Network, the use of multiplication neurons (M neurons) as proposed by Li et al. [27] bring better representation ability and computational power than do summation neurons. Erol et al. greatly reduced the number of hidden layer nodes through adding the multiplicative neuron in a new recurrent neural network model [28].

In this paper, the main contribution is proposing a new sequential feature extraction method based on the DWT, PSR and SVD of covariance matrix, and building a classifier based on ELM with multiplication neurons (M-ELM). Firstly, EEG signals are decomposed into several sub-signals by DWT in time–frequency domain. Wavelet coefficients of the several sub-signals are then produced. Then the sub-band signals are extended from low dimension to high dimension by using PSR. Through the mutual information and C–C method analysis, fixed delay times and small embedding dimension are then suggested for use. These can separate the vectors in PSR method. Therefore, one dimension sub-band wavelet coefficients are reconstructed in 2D and 3D phase space. Moreover, SVD based covariance matrix of phase space matrix is suggested for use in replacement of other geometry statistical analysis methods such as the confidence ellipse area and Euclidean distance. Covariance matrix of phase space can be used to express the relationship between dimensions. The singular values remove redundant dimensions and noises to achieve the dimensionality reduction. The singular values from the covariance matrix, namely the energy of the epileptic seizure signals are larger than normal EEG signals. Finally, the feature values are input into the M-ELM classifier. This can not only increase the nonlinear expression ability of hidden layer nodes, but also solve the local optimum problem. Seven experimental cases for the EEG database from the University of Bonn [29] are used. Experiments are conducted in different epoch sizes and are compared with other existing methods to test the performance of the proposed method.

The rest of the paper is organized as follows. The principles of the basic extreme learning machine and improved multiplicative extreme learning machine (M-ELM) are described in Section 2. In Section 3, the EEG data is introduced. A sequential processing method is proposed in Section 4, where the DWT, PSR, extraction methods with covariance matrix and SVD as well as the M-ELM classifier are described. To show the superiority of the proposed method, numerical results and comparison of classification accuracy with others classification methods are presented in Section 5. Finally, the conclusion is presented in Section 6.