中国物理B ›› 2020, Vol. 29 ›› Issue (8): 80501-080501.doi: 10.1088/1674-1056/ab9287

• SPECIAL TOPIC—Ultracold atom and its application in precision measurement • 上一篇    下一篇

Patterns of cross-correlation in time series: A case study of gait trails

Jia Song(宋佳), Tong-Feng Weng(翁同峰), Chang-Gui Gu(顾长贵), Hui-Jie Yang(杨会杰)   

  1. Business School, University of Shanghai for Science and Technology, Shanghai 200082, China
  • 收稿日期:2020-02-01 修回日期:2020-05-08 出版日期:2020-08-05 发布日期:2020-08-05
  • 通讯作者: Hui-Jie Yang E-mail:hjyang@usst.edu.cn
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Grant Nos. 11805128, 11875042, 11505114, and 10975099), the Program for Professor of Special Appointment (Orientational Scholar) at Shanghai Institutions of Higher Learning, China (Grant Nos. D-USST02 and QD2015016), and the Shanghai Project for Construction of Top Disciplines, China (Grant No. USST-SYS-01).

Patterns of cross-correlation in time series: A case study of gait trails

Jia Song(宋佳), Tong-Feng Weng(翁同峰), Chang-Gui Gu(顾长贵), Hui-Jie Yang(杨会杰)   

  1. Business School, University of Shanghai for Science and Technology, Shanghai 200082, China
  • Received:2020-02-01 Revised:2020-05-08 Online:2020-08-05 Published:2020-08-05
  • Contact: Hui-Jie Yang E-mail:hjyang@usst.edu.cn
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Grant Nos. 11805128, 11875042, 11505114, and 10975099), the Program for Professor of Special Appointment (Orientational Scholar) at Shanghai Institutions of Higher Learning, China (Grant Nos. D-USST02 and QD2015016), and the Shanghai Project for Construction of Top Disciplines, China (Grant No. USST-SYS-01).

摘要:

A complex system contains generally many elements that are networked by their couplings. The time series of output records of the system's dynamical process is subsequently a cooperative result of the couplings. Discovering the coupling structure stored in the time series is an essential task in time series analysis. However, in the currently used methods for time series analysis the structural information is merged completely by the procedure of statistical average. We propose a concept called mode network to preserve the structural information. Firstly, a time series is decomposed into intrinsic mode functions and residue by means of the empirical mode decomposition solution. The mode functions are employed to represent the contributions from different elements of the system. Each mode function is regarded as a mono-variate time series. All the mode functions form a multivariate time series. Secondly, the co-occurrences between all the mode functions are then used to construct a threshold network (mode network) to display the coupling structure. This method is illustrated by investigating gait time series. It is found that a walk trial can be separated into three stages. In the beginning stage, the residue component dominates the series, which is replaced by the mode function numbered M14 with peaks covering ~680 strides (~12 min) in the second stage. In the final stage more and more mode functions join into the backbone. The changes of coupling structure are mainly induced by the co-occurrent strengths of the mode functions numbered as M11, M12, M13, and M14, with peaks covering 200-700 strides. Hence, the mode network can display the rich and dynamical patterns of the coupling structure. This approach can be extended to investigate other complex systems such as the oil price and the stock market price series.

关键词: intrinsic mode function, mode network, gait time series

Abstract:

A complex system contains generally many elements that are networked by their couplings. The time series of output records of the system's dynamical process is subsequently a cooperative result of the couplings. Discovering the coupling structure stored in the time series is an essential task in time series analysis. However, in the currently used methods for time series analysis the structural information is merged completely by the procedure of statistical average. We propose a concept called mode network to preserve the structural information. Firstly, a time series is decomposed into intrinsic mode functions and residue by means of the empirical mode decomposition solution. The mode functions are employed to represent the contributions from different elements of the system. Each mode function is regarded as a mono-variate time series. All the mode functions form a multivariate time series. Secondly, the co-occurrences between all the mode functions are then used to construct a threshold network (mode network) to display the coupling structure. This method is illustrated by investigating gait time series. It is found that a walk trial can be separated into three stages. In the beginning stage, the residue component dominates the series, which is replaced by the mode function numbered M14 with peaks covering ~680 strides (~12 min) in the second stage. In the final stage more and more mode functions join into the backbone. The changes of coupling structure are mainly induced by the co-occurrent strengths of the mode functions numbered as M11, M12, M13, and M14, with peaks covering 200-700 strides. Hence, the mode network can display the rich and dynamical patterns of the coupling structure. This approach can be extended to investigate other complex systems such as the oil price and the stock market price series.

Key words: intrinsic mode function, mode network, gait time series

中图分类号:  (Time series analysis)

  • 05.45.Tp
89.75.Fb (Structures and organization in complex systems)