A novel approach of dependence measure for complex signals

Abstract

The distance correlation (DC) statistics is capable of describing the nonlinear correlation between random variables, which is the extension and reinforcement of the existing Pearson correlation coefficient, Spearman rank correlation coefficient, Kendall coefficient of concordance, etc. However, there are difficulties in using the DC statistics to measure the dynamical features of complex signals directly. So in this work, we introduce the refined distance correlation (RDC). Motivated by the cross-sample entropy (CSE), a state-of-the-art measure, we propose the dependence measure (DM) based on the RDC and the phase space reconstruction theory, aiming to capture linear and nonlinear dynamical features from various kinds of complex signals with higher accuracy. The RDC also includes the modified version of distance dependence statistics that overcomes the natural defect of the original DC. We first apply the RDC and the DM into simulation signals to testify whether they are effective in detecting different dynamical features. Afterward, we apply our methods to analyze real-world data. We affirm that our methods are capable of obtaining more detailed information by comparing it to the CSE. Finally, we combine the DM and the CSE to construct the DM–CSE plane. By applying it to the existing data, more distinctive and rational clustering results of complex systems are obtained.