Epilepsy Diagnosis Using Probability Density Functions of EEG Signals U. Orhan Gaziosmanpasa University Tokat, 60250, TURKEY umutorhan@hotmail.com M. Hekim Gaziosmanpasa University Tokat, 60250, TURKEY mhekim@gop.edu.tr M. Ozer Zonguldak Karaelmas University Zonguldak, 67100, TURKEY mahmutozer2002@yahoo.com I. Provaznik Brno University of Technology Brno, 61200, CZECH REPUBLIC provazni@feec.vutbr.cz Abstract—In this paper, the equal frequency discretization (EFD) based probability density approach was proposed to be used in the diagnosis of epilepsy from electroencephalogram (EEG) signals. For this aim, EEG signals were decomposed by using the discrete wavelet discretization (DWT) method into subbands, the coefficients in each subband were discretized to several intervals by EFD method, and the probability density of each subband of each EEG segment was computed according to the number of coefficients in discrete intervals. Then, two probability density functions were defined by means of the curve fitting over the probability densities of the sets of both healthy subjects and epilepsy patients. EEG signals were classified by applying the mean square error (MSE) criterion to these functions. The result of the classification was evaluated by using the ROC analysis, which indicated 82.50% success in the diagnosis of epilepsy. As a result, the EFD based probability density approach may be considered as an alternative way to diagnose epilepsy disease on EEG signals. Keywords- EEG signals; wavelet transform; epilepsy; equal frequency discretization; probability density; mean square error; curve fitting I. INTRODUCTION Epilepsy is a kind of crucial neurological disease. Epilepsy patients are subjected to epileptic seizures caused by abnormal electrical discharges leading to uncontrollable movements, convulsions and the loss of conscious [1]. Electroencephalogram (EEG) signals taken from the EEG recording systems are used in the analysis of epileptic activities of the brain. Visual analysis of the signals is very difficult since EEG recording systems generate very large amounts of data. Therefore, there are many studies focused on the computer basis automated model for the analysis of EEG signals [1-17]. Most of EEG based analysis models requires the time, the frequency or the time-frequency analysis followed by a linear or non-linear classifier [2]. The methods using the features in the time-frequency domain usually provide higher successes than the others in the classification studies on EEG signals. However, the success of classification depends on both the classifier and the features to be applied into that classifier. Most of the classifiers used in the analysis of EEG signals utilize the statistical features obtained by the time-frequency analysis of EEG signals [3-9] because a time-frequency analysis method provides both time and frequency views of a signal simultaneously, which makes it possible to accurately capture and localize temporary features in the data like the epileptic spikes [9]. As the time-frequency analysis method, the discrete wavelet transform (DWT) is widely preferred in the analysis of EEG signals. The DWT method is a spectral analysis technique used for analyzing non-stationary signals, and provides time-frequency representation of the signals by decomposing the signals into a set of subbands through consecutive high-pass and low-pass filtering of the time domain signal. In addition, in order to extract some details about these subbands of EEG signals, they can be discretized by a discretization method. Equal frequency discretization (EFD) is widely preferred method in the discretization [18, 19] since it is capable of providing the probability distribution of continuous or discrete signals. In this study, EEG signals are decomposed by DWT into subbands, each subband is discretized by the EFD method, and the probability density of each subband of each EEG segment is computed. Two probability density functions are defined according to the probability densities of both the set of healthy subjects and the set of epilepsy patients. EEG signals are classified by applying the mean square error (MSE) criterion to these two functions. The remaining of the paper is organized as follows. Section 2 presents the EEG dataset, discrete wavelet transform, EFD based probability density approach and validity criterion used in the study. In Section 3, the results and discussion of the study are given in detail. Finally, we conclude this paper in Section 4. II. MATERIAL AND METHOD A. EEG Dataset In this study, the EEG data described in [17] was used for the diagnosis of epilepsy. The complete data consists of five sets (A, B, C, D, and E). Each one contained 100 EEG segments sampled in the frequency of 173.60 Hz during 23.6 sec. Sets A (eyes open) and B (eyes closed) were extra- cranially taken from five healthy subjects. Sets C, D and E were intra-cranially taken from five epilepsy patients. While sets D and C contained the EEG activity measured in seizure- free intervals from epileptic hemisphere and the opposite 626 978-1-61284-922-5/11/$26.00 ©2011 IEEE