Determination of the degree of three-dimensional Poincaré section in Epileptic Seizure Detection by EEG

Using methods based on nonlinear dynamics such as Poincare Section, can be useful in detecting dynamic biological systems. Selecting a suitable Poincare surface is a critical step in data analysis. Often finding an appropriate Position for Poincare Section needs to set different parameters. When the geometry of Poincare Surface picks the information related to the Stretching and folding, a better discrimination can be performed for the system states. The objective of this paper is to study the effect of position and degree of Poincare surface in Epileptic Seizure Detection. The Poincare surface resulting in the best classification is selected as the optimal section. Accordingly, the phase space of the EEG Segments Reconstructed in three dimension, firstly. Then, a set of Poincare surfaces with 400 different conditions of degree selected to cut the trajectory and Geometric features Extracted from the points of intersection on each surface. Afterward, extracted features from the Poincare section are applied to SVM classifier. Pearson correlation analysis was performed to analyze the relationship between the classification performance and degree of Poincare section. Certain behavior can be observed by increasing the Surface degree in output classifier. In this way, the increasing and then decreasing pattern were observed by increasing the Surface degree in two Directions of Surface. The results showed that the equation of optimal Poincare Section for m=12 and n=6 gives the accuracy of 96.6%.