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Sampling frequency dependent visibility graphlet approach to time series.

Yan Wang1, Tongfeng Weng1, Shiguo Deng1

  • 1Business School, University of Shanghai for Science and Technology, Shanghai 200093, People's Republic of China.

Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

This study introduces a new method, sampling frequency dependent visibility graphlets, to analyze time series evolution. It reveals how sampling frequency impacts complex network analysis, offering new insights into system dynamics.

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Area of Science:

  • Complex Systems Analysis
  • Time Series Analysis
  • Network Science

Background:

  • Complex network-based time series analysis is gaining attention for understanding system evolution.
  • Traditional graphlet-based analysis segments time series and maps them to graphlets to represent states.
  • The influence of sampling frequency on these evolutionary behaviors remains an open question.

Purpose of the Study:

  • To propose a novel concept, the sampling frequency dependent visibility graphlet, to address the impact of sampling frequency on time series analysis.
  • To investigate how varying sampling periods (delays) alter state transition networks and reveal time series characteristics at different scales.
  • To demonstrate the applicability of this method across diverse datasets, including mathematical models and empirical data.

Main Methods:

  • Introduced the sampling frequency dependent visibility graphlet by extracting new series with specified delays between successive elements.
  • Applied the graphlet-based approach to obtain state transition networks from these modified series.
  • Analyzed transition networks derived from fractional Brownian motion, logistic map, Rössler system, and empirical sentence length series.

Main Results:

  • Fractional Brownian motions exhibit a consistent backbone pattern in transition networks, with subtle quantitative differences based on Hurst exponents.
  • The sentence length series shows the backbone pattern but with significant differences in linkage strengths compared to fractional Brownian motions.
  • Logistic map and Rössler system trajectories display distinct patterns and structural changes in transition networks as the sampling period varies, revealing system-specific dynamics.

Conclusions:

  • The sampling frequency dependent visibility graphlet method provides novel insights into time series trajectories by capturing scale-dependent behaviors.
  • This approach effectively differentiates characteristics across various time series, including mathematical models and empirical data.
  • The method holds potential for analyzing diverse complex systems such as brain activity and financial markets.