Transition-based complexity-entropy causality diagram: A novel method to characterize complex systems

Abstract

Complexity-entropy causality plane (CECP) and ordinal transition network (OTN) are both crucial tools to reveal the characteristics of time series and distinguish complex systems. However, when the parameters of the system to be distinguished have a wide range of values, the distinguishing function of CECP is weakened. Therefore, we propose a new measure called transition Fisher information (TFI) based on the probability transition matrix in OTN. The TFI is combined with conditional entropy of ordinal patterns and complexity measure to form a novel three-dimensional graph, called transition-based complexity-entropy causality diagram(TB-CECD). These three statistics depict the complex system from different angles. Through simulation experiments, we prove that even if the parameters of complex systems are wide-ranging, the systems of different properties can be assigned to different areas of the graph. Moreover, we find that the trace of the transition probability matrix can be seen as a function of time delay and used to reflect the periodic information of the system. For applications, the proposed methods are applied to vehicle dynamic response data to diagnose periodic short-wave defects such as rail corrugation. The financial time series and Electroencephalographic (EEG) time series are also researched.