Modeling of seizure and seizure-free EEG signals based on stochastic differential equations

seizures commonly occurs in epileptic patients and decrease their quality of life. Investigating past attacks and predict future seizures can be done by exact classification between healthy and seizure based segments in electroencephalograph (EEG) recordings of these patients. Modeling EEG signal can help to extract discriminative features from it. These features make automatic classification more accurate. In this paper we propose a new modeling for EEG signals based on stochastic differential equations (SDE). In this statistical modeling, EEG signals are modeled with a self-similar fractional Levy stable process due to their inherent self-similarity. These processes are considered as response of SDE to the zero mean white symmetric alpha stable noise and inversely, by applying a derivative operator on these processes this white noise could be obtained again. We use a scale invariant fractional derivative operator for this purpose. Having fitted a probability distribution to the histogram of EEG signal after derivation, parameters of fitted histogram can be applied as features for classification task. We modeled healthy and epileptic segments of EEG signal from Bonn University database, and Neurology and Sleep Centre of New Delhi database. As an application of proposed model, we used features obtained from modeled signals to train an SVM classifier. Experimental result revealed highest classification of 99.8% for Bonn University database and 99.1% for Sleep Centre of New Delhi database, between normal and epileptic EEG signals. In conclusion, the proposed model is simple (does not require any decomposition of EEG signals), accurate and computationally efficient.