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Jensen-Inaccuracy Information Measure.

Omid Kharazmi1, Faezeh Shirazinia1, Francesco Buono2

  • 1Department of Statistics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran.

Entropy (Basel, Switzerland)
|March 29, 2023
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Summary
This summary is machine-generated.

This study introduces the Jensen-inaccuracy measure for information theory. It explores its properties, connections to other measures, and applications in optimization and image processing.

Keywords:
Jensen–inaccuracy measureRényi entropyaverage entropyinaccuracy measureoptimal information

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Area of Science:

  • Information Theory
  • Mathematical Analysis

Background:

  • Existing information measures have limitations in certain applications.
  • The need for novel measures to capture specific data properties is recognized.

Purpose of the Study:

  • Introduce and analyze the novel Jensen-inaccuracy measure.
  • Investigate its relationship with established information measures.
  • Demonstrate its utility in optimization and real-world data analysis.

Main Methods:

  • Theoretical examination of the Jensen-inaccuracy measure's properties.
  • Comparative analysis with existing information measures.
  • Application in three distinct optimization problems.
  • Empirical validation using image processing examples.

Main Results:

  • The Jensen-inaccuracy measure is formally defined and its characteristics are detailed.
  • Connections between Jensen-inaccuracy, inaccuracy, and other information measures are established.
  • Optimal information properties of arithmetic mixture distributions are shown using the inaccuracy measure.
  • Numerical results demonstrate the measure's performance in image processing tasks.

Conclusions:

  • The Jensen-inaccuracy measure offers a valuable addition to the field of information theory.
  • Its properties and applications provide new insights for data analysis and optimization.
  • The measure shows practical relevance in fields like image processing.