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Point Divergence Gain and Multidimensional Data Sequences Analysis.

Renata Rychtáriková1, Jan Korbel2,3,4, Petr Macháček1

  • 1Institute of Complex Systems, South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses, Kompetenzzentrum MechanoBiologie in Regenerativer Medizin, Faculty of Fisheries and Protection of Waters, University of South Bohemia in České Budějovice, Zámek 136, 373 33 Nové Hrady, Czech Republic.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

We developed new information-entropy measures to analyze changes in image data over time. These novel variables help characterize complex spatio-temporal patterns in multidimensional datasets.

Keywords:
Rényi entropydata processingpoint divergence gain (PDG)

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Area of Science:

  • Information Theory
  • Image Analysis
  • Data Science

Background:

  • Analyzing spatio-temporal changes in multidimensional data is crucial for understanding dynamic systems.
  • Existing methods may not fully capture the nuances of evolving data distributions.
  • Rényi entropy provides a flexible framework for quantifying information-theoretic properties.

Purpose of the Study:

  • Introduce novel information-entropic variables: Point Divergence Gain (Ω α (l → m)), Point Divergence Gain Entropy (I α), and Point Divergence Gain Entropy Density (P α).
  • Describe spatio-temporal changes between consecutive discrete multidimensional distributions.
  • Apply these variables to analyze and characterize image datasets.

Main Methods:

  • Derive new variables from Rényi entropy.
  • Simulate the behavior of Point Divergence Gain (Ω α (l → m)) for typical distributions.
  • Apply the developed variables (Ω α (l → m), I α, P α) to analyze series of multidimensional datasets.

Main Results:

  • Novel information-entropic variables (Ω α (l → m), I α, P α) were successfully defined.
  • The behavior of Ω α (l → m) was simulated, demonstrating its utility.
  • These variables were applied to characterize both computer-generated and real-world image data series.

Conclusions:

  • The introduced Point Divergence Gain variables offer a new approach to quantifying spatio-temporal changes.
  • These variables are effective for analyzing and characterizing complex multidimensional image datasets.
  • The framework provides enhanced tools for information-theoretic analysis of evolving data.