Metodología para evaluar el difeomorfismo de un atractor caótico usando el filtro de kalman en señales fisiológicas

Abstract

In order to characterize physiological signals, which may have highly nonlinear structures, it’s common to use methodologies derived from fractal techniques that make part of complexity analysis. This work proposes is proposed an evaluation function based on measuring the capacity of prediction of a neural network trained with Kalman filter to predict points in a reconstructed state space attractor, so measuring the quality of the attractor from a onedimensional signal. We propose use of statistic measures such as Kullback –Leibler, Kolmogorov-Smirnov and Hellinger to determine difference between the embedded statistic structure in the predicted points and the original signal points. Results were obtained on attractor reconstruction from ECG signals of MIT-BIH database and EEG signals obtained from Clinic for Epileptologie Epileptologie Bonn University database. In this way, it was possible to evaluate the prediction capacity corresponding to reconstruct attractors from records, from which we concluded that an attractor with high capacity of time series prediction implies good embedding properties in state space.