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    Mathematical and Computational Applications , Vol. 10, No. 1, pp. 57-70, 2005. © Association for Scientific Research NEURAL NETWORK CLASSIFICATION OF EEG SIGNALS BY USING AR WITH MLE PREPROCESSING FOR EPILEPTIC SEIZURE DETECTION Abdulhamit Subasi a , M. Kemal Kiymik  a* , Ahmet Alkan a , Etem Koklukaya  b  e-mail : {asubasi, mkemal, aalkan}; a Department of Electrical and Electronics Engineering, Kahramanmara ş  Sütçü İ mam University, 46100 Kahramanmara ş , Turkey.  b Department of Electrical and Electronics Engineering, Sakarya University   54187 Sakarya, Turkey. Abstract- The purpose of the work described in this paper is to investigate the use of autoregressive (AR) model by using maximum likelihood estimation (MLE) also interpretation and performance of this method to extract classifiable features from human electroencephalogram (EEG) by using Artificial Neural Networks (ANNs). ANNs are evaluated for accuracy, specificity, and sensitivity on classification of each patient into the correct two-group categorization: epileptic seizure or non-epileptic seizure. It is observed that, ANN classification of EEG signals with AR gives better results and these results can also be used for detecting epileptic seizure. Keywords-   EEG, Autoregressive method (AR), Maximum likelihood estimation (MLE), Artificial Neural Networks (ANN). 1.   INTRODUCTION EEG signals involve a great deal of information about the function of the brain. But classification and evaluation of these signals are limited. Since there is no definite criterion evaluated by the experts, visual analysis of EEG signals is insufficient. Since routine clinical diagnosis needs to analysis of EEG signals, some automation and computer techniques have been used for this aim. Since the early days of automatic EEG processing, representations based on a Fourier transform have been most commonly applied. This approach is based on earlier observations that the EEG spectrum contains some characteristic waveforms that fall primarily within four frequency bands— delta (< 4 Hz), theta (4–8 Hz), alpha (8–14 Hz), and beta (14–30 Hz). Such methods have proved  beneficial for various EEG characterizations, but fast Fourier transform (FFT), suffer from large noise sensitivity. Parametric power spectrum estimation methods such as AR, reduces the spectral loss problems and gives better frequency resolution. Also AR method has an advantage over FFT that, it needs shorter duration data records than FFT [1,2]. Also it is faster than Continuos Wavelet transform techniques, especially in real time applications [18].    Numerous other techniques from the theory of signal analysis have been used to obtain representations and extract the features of interest for classification purposes. Neural networks and statistical pattern recognition methods have been applied to EEG analysis. Over the past two decades much research has been done with the use of conventional   A. Subasi, M. K. Kiymik, A. Alkan and E. Koklukaya 58 temporal and frequency analyses measures in the detection of epileptic form activity in EEGs and comparatively good results have been obtained [1-6].  Neural network detection systems have been proposed by a number of researchers [7-23]. Pradhan[9] uses the raw EEG as an input to a neural network while Weng [8] uses the features proposed by Gotman [6] with an adaptive structure neural network, but his results show a poor false detection rate. Petrosian, et al., [12] showed that the ability of specifically designed and trained recurrent neural networks (RNN), combined with wavelet  preprocessing, to predict the onset of epileptic seizures both on scalp and intracranial recordings. Esteller [23] uses linear predictor to find AR coefficients as an input to ANN. In this study we used maximum likelihood estimation (MLE) to find AR parameters and after that we used these AR coefficients as an input to ANN. The purpose of the work described in this paper is to investigate the practicality of using an AR model by using MLE to extract classifiable features from human EEG. The success of this study depends on finding a signal representation contains the information needed to accurately classify epileptic seizure. Here, AR model with MLE was used to define representations. Various feature based on this model was classified with a multilayer, feedforward, neural network using the error back-propagation training algorithm. Discrimination was performed between a single pair of tasks. An AR with MLE representation resulted in the better classification percentages than FFT representation. 2.   MATERIALS AND METHOD 2.1. EEG Data Acquisition and Representation Epileptic seizure is an abnormality in EEG recordings and is characterized by brief and episodic neuronal synchronous discharges with dramatically increased amplitude. This anomalous synchrony may occur in the brain locally (partial seizures) which is seen only in a few channels of the EEG signal, or involving the whole brain (generalized seizures) which is seen in every channel of the EEG signal. Subjects in different age group were recruited for this study. They were known epileptics with uncontrolled seizures and were admitted to the neurology department of the Medical Faculty Hospital of Dicle University. These signals belong to several healthy and unhealthy (epileptic patients) persons. The signals are collected by a data acquisition system which contains data acquisition card (PCI MIO-16-E+ type), signal processors and a  personnel computer. Data can be taken in to computer memory quickly by using this card which is connected to PCI data bus of the computer. For this system LabVIEW  programming language was used. The system provides real time data processing. EEG signals are analyzed by using spectral analysis methods to diagnose some cerebral diseases. The power spectral density of the signal P(f) found by applying     Neural Network Classification of EEG Signals 6   59 Figure. 1. The scheme of the EEG data acquisition system. conventional and modern spectral analysis methods such as FFT and AR. The data acquisition system for the processing of EEG signals is shown in Fig. 1. 2.2. Autoregressive parameter estimation and MLE In the AR model, to find out model parameters Levinson-Durbin algorithm which makes use of the solution of the Yule-Walker equations is used. Autocorrelation estimation is used for the solution of these equations. After those autocorrelation, AR model  parameters are estimated. To do that biased form of the autocorrelation estimation is used which is given as 0..),........()( 1 *10 ≥+=  ∑ −−= mmn xn x  N r  m N n xx  (1) The aim now is to estimate the AR model parameters by using MLE in the solution of the Yule-Walker equations from a record of EEG data. If the maximum likelihood estimate of a  parameter exists under regular conditions, it is consistent, asymptotically unbiased, efficient, and normally distributed. Unfortunately, the maximum likelihood (ML) estimator is often too cumbersome to obtain. As this is the case for the EEG model, it is proposed to estimate the model parameters by maximizing an approximation of the log-likelihood function, known as Whittle’s approximation, the derived estimator is expected to retain the  properties associated with the ML estimator in an asymptotic sense, but with much less complexity. In fact, Whittle’s estimate asymptotically retains the properties of the ML estimate for Gaussian random processes, but this is not generally true for the non-Gaussian case [2]. In many cases it is difficult to evaluate the MLE of the parameter whose power spectrum density function (PSDF) is Gaussian due to the need to invert a large dimension   A. Subasi, M. K. Kiymik, A. Alkan and E. Koklukaya 60 covariance matrix. For example, if   ( )  )( c ,~ x  θ  0  Ν , the MLE of θ   is obtained by maximizing ]).(.2/1[ 2/ 1 ))(det(.)2( 1);(  X c X n t  ec x P   θ  θ π θ  − − =  (2) If the covariance matrix cannot be inverted in closed form, then a search technique will require inversion of the NxN matrix for each value of θ  to be searched. An alternative approximate method can be applied when x is data from a zero mean random process, so that covariance matrix is Toeplitz. In such a case, the asymptotic log-likelihood function is given by ∫ − +−= 2/12/1 ])()()([ln22ln2);(ln df  f  P  f  I  f  P  N  N  x P   xx xx π θ   (3) where 210)2( ).(1)(  ∑ −=− =  N n fn j en x N  f  I   π   is the periodogram of the data and P xx (f) is the power spectral density (PSD). The dependence of the log-likelihood function on θ   is through the PSD. Differentiation of (3)  produces the necessary conditions for MLE ∫ −  ∂∂−−=∂∂ 2/12/12 )()()()(12);(ln df  f  P  f  P  f  I  f  P  N  x P  i xx xx xxi  θ θ θ   (4) or 0)()()()(1 2/12/12  =∂∂− ∫ − df  f  P  f  P  f  I  f  P  i xx xx xx  θ   (5) The second derivative allows the Newton-Raphson or scoring method may be implemented using the asymptotic likelihood function. This leads to simpler iterative procedures and is commonly used in practice. In this study, to find MLE asymptotic form of the log-likelihood given by (3) is used. Since the PSD is 22 )()(  f  A f  P  u xx δ  =  (6) After some calculations and derivations, the estimated auto correlation function is, ≥−≤+=  ∑ −−=∧  N k  N k k n xn x  N k  R k  N n xx ....................................0 1).....()( 1)( 10  (7)
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