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On system behaviour using complex networks of a compression algorithm.

David M Walker1, Debora C Correa1, Michael Small1

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We developed a novel method to analyze complex systems using data compression to build networks from time series data. This approach effectively identifies system dynamics and behavioral changes, offering efficient data characterization.

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Area of Science:

  • Complex Systems Science
  • Network Science
  • Data Analysis

Background:

  • Characterizing complex systems often relies on analyzing their time series data.
  • Traditional methods may struggle with the scale and complexity of long time series.
  • Identifying dynamical behavior and transitions is crucial for understanding system dynamics.

Purpose of the Study:

  • To introduce a new method for constructing complex networks from scalar time series.
  • To demonstrate the utility of network properties as discriminating statistics for complex systems.
  • To apply the method for identifying behavioral transitions in electroencephalogram (EEG) recordings and chaotic systems.

Main Methods:

  • Utilizing a data compression algorithm to generate complex networks from scalar time series data.
  • Analyzing the structure and statistics of the constructed networks.
  • Applying coarse-grained quantization for scale-dependent characterization.
  • Testing the method on systems with known dynamics and real-world EEG data.

Main Results:

  • The constructed networks reveal properties useful for characterizing complex systems.
  • A specific network property serves as a valuable discriminating statistic in hypothesis testing.
  • The method successfully identified behavioral transitions in EEG data.
  • Changes in a chaotic system due to a bifurcation parameter were detected.

Conclusions:

  • Network construction from time series via data compression offers an efficient way to characterize complex systems.
  • The approach provides a scale-dependent analysis and compresses salient features of long time series.
  • This method has practical applications in neuroscience and the study of dynamical systems.