Multiscale permutation mutual information quantify the information interaction for traffic time series
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ORIGINAL PAPER
Multiscale permutation mutual information quantify the information interaction for traffic time series Yi Yin · Xi Wang · Qiang Li · Pengjian Shang · He Gao · Yan Ma
Received: 12 January 2019 / Accepted: 23 September 2020 © Springer Nature B.V. 2020
Abstract The purpose of this study was to introduce a method in extracting and quantifying the information flow in complex system, which takes into account the temporal structure of the time series at multiple scales. It is important that the method should be able to reflect the intrinsic mechanism of information interaction faithfully. The proposed multiscale permutation mutual information (MPMI) method studies the mutual information based on permutation pattern and multiscale concept from multiscale sample entropy and is initially tested on artificially generated signals for proof of concept by comparing the MPMI results of the iterative amplitude adjusted Fourier transform surrogates and the original series. It is subsequently applied to quantify the information interaction of traffic time series. MPMI results can detect the relationship between neighboring detectors and the effect of traffic Y. Yin (B)· X. Wang · Q. Li School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, People’s Republic of China e-mail: [email protected] P. Shang School of Science, Beijing Jiaotong University, Beijing 100044, People’s Republic of China H. Gao Department of Sleep Medicine, the PLA Air Force Medical Center, Beijing 100142, People’s Republic of China Y. Ma Division of Interdisciplinary Medicine and Biotechnology, Department of Medicine, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA 02215, USA
accidents on information interaction between speed and volume. MPMI method uncovers the information interaction and provides valuable insight into the underlying mechanisms in traffic system. Keywords Multiscale permutation mutual information (MPMI) · Information interaction · Artificial time series · Traffic time series
1 Introduction Considerable complex systems are often constrained by the external environment and the interaction between internal variables. Traffic system as one of typical complex systems [1,2] has attracted considerable interests. As the intelligent transportation systems (ITS) technologies advance, a large amount of traffic data can be obtained and the development of study on the traffic data has been growing rapidly in recent years. Numerous techniques such as chaotic analysis [3], complex network [4], and nonlinear method [5] have been applied on the study of traffic system behavior. Understanding the relationship between systems or between individual components in the single systems is of great importance for analyzing the practical complex systems. In recent years, many techniques have been proposed to study the information interaction between systems and variables within the system: (i) time series-based correlation, such as linear correlation function and detrended cros
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