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Tangle: A metric for quantifying complexity and erratic behavior in short time series.

Robert G Moulder1, Katharine E Daniel1, Bethany A Teachman1

  • 1Department of Psychology.

Psychological Methods
|January 28, 2021
PubMed
Summary

A new method called tangle quantifies temporal complexity in short time series, overcoming technical hurdles in psychological research. This approach aids in understanding complex dynamics in psychological data.

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Area of Science:

  • Psychological science
  • Complexity science
  • Time series analysis

Background:

  • Temporal complexity describes erratic or emergent time series dynamics.
  • Current complexity quantification methods are often computationally intensive and require large datasets, limiting their use in psychology.
  • Understanding time-based dynamics is crucial but challenging with existing tools.

Purpose of the Study:

  • To introduce a novel method, tangle, for quantifying temporal complexity.
  • To enable complexity analysis in short time series typical of psychological studies.
  • To provide a computationally accessible tool for psychological research.

Main Methods:

  • Tangle quantifies dissimilarity from simple periodic motion using a 3D time delay embedding.
  • The method involves iterative scaling and matrix multiplication until convergence.
  • Applied to mathematical series, emotional stability/anxiety data (65 participants, 5 weeks), and positive affect data during depression.

Main Results:

  • Tangle successfully distinguished complex temporal systems in time series with as few as 50 samples.
  • Demonstrated efficacy on diverse datasets, including psychological measures.
  • The method proved robust across simulations and real-world data.

Conclusions:

  • Tangle offers a reliable quantification of irregular time series behavior.
  • It is technically simple to implement and computationally efficient.
  • Tangle can uncover meaningful insights from psychological time series data, overcoming previous limitations.