A new algorithm for Largest Lyapunov Exponent determination for noisy chaotic signal studies with application to Electroencephalographic signals analysis for epilepsy and epileptic seizures detection

Electroencephalographic signals (EEG) are main examination of brain disease, because of their simple portability and their important temporal resolution of milliseconds or less. Nevertheless, the study of EEGs is confronted mainly with two problems: its complex behavior, which is considered in this paper due to its chaotic origin, and being contaminated by different types of noise from different sources. Our paper is thus carried out dealing with mentioned issues, we propose an algorithm for Largest Lyapunov Exponent (LLE) determination based on that of A. Wolf. In fact, LLE is an efficient tool for chaotic signal analysis. Our algorithm permits to study noisy chaotic signal. The proposed method was evaluated using a chaotic signal, obtained from the Logistic Map, for different values of the bifurcation parameter, we reach a low error rate in LLE determination using the proposed method (PLLE). Later, we use a noisy chaotic signal obtained from an additive noise to the previous signal, again PLLE leads to a perfect estimation of LLE, with a weak dependence on noise. The performance of the proposed PLLE, for LLE estimation, is also confirmed through other chaotic attractors, Hénon, Rössler and Lorenz. We then propose a supervised machine learning model for epilepsy and seizure detection based on PLLE, kernel tricks and features reduction using the benchmark EEG database provided by the University of Bonn. Comparisons with various state-of-the-art methods demonstrate the importance of our proposed method, which achieves 100% accuracy in different classification cases, runs fast and uses 4 features.