Volumetric behavior quantification to characterize trajectory in phase space

This paper presents a methodology to extract a number of quantifier features to characterize volumetric behavior of trajectories in phase space. These features quantify expanding and contracting behaviors and complexity that can be used in nonlinear and chaotic signals classification or clustering problems. One of the features is directly extracted from the distance matrix and seven features are extracted from a matrix that is subsequently obtained from the distance matrix. To illustrate the proposed quantifiers, Mackey-Glass time series and Lorenz system were employed and feature evaluation was performed. It is shown that the proposed quantifier features are robust to different initializations and can quantify volumetric behavior characteristics. In addition, the ability of these features to differentiate between signals with different parameters is compared with some common nonlinear features such as fractal dimensions and recurrence quantification analysis features.