A new approach to automatically generate optimal Poincaré plane from discrete time series

In biologic systems, it is not possible to access the whole system information directly and system dynamics usually need to be predicted from their time series. One approach to analyze these dynamics is to embed time series and extract samples by Poincaré plane in embedding space. In order to extract the best samples from the system, selecting an appropriate plane is crucial. There is no unique way to choose a Poincaré plane and it is highly dependent to the system dynamics. In this study; a new approach is introduced to automatically generate an optimum Poincaré plane from discrete time series, based on maximum transferred information. For this purpose, time series are first embedded; then a parametric Poincaré plane is defined and finally optimized using genetic algorithm. This approach is tested on epileptic EEG signals and the optimum Poincaré plane is obtained with more than 97 % data information transferred.