Validity analysis of knowledge acquisition from nonlinear time series by symbolization

When making symbol inference and analyzing dynamical system, as a key step, symbolization is inevitable. All sorts of symbolization methods are applied to measured data of non-linear system, and they seem to help us understanding complex system effectively. Reconstructed phase space is a representation of non-linear structure hidden in dynamical system. In this paper the contour of the phase space is considered as the evaluating standard to check the validity of symbolization. Three typical examples, the solution of Duffing equation, laser generated data, ECG, and their corresponding symbol series, are analyzed with embedding algorithm. From all the phase space figures, an intuitional conclusion can be drawn that symbolization destroys the non-linear structures. If symbolization was necessary when studying non-linear time series, we think that, the results would be credible partially unless additional evidences are on hand. If someone had to make use of symbolization, equal interval method would be a better choice to retain the rude non-linear structure as much as possible, and the results need to be interpreted carefully.