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The Entropy Universe
Maria Ribeiro1,2, Teresa Henriques3,4, Luísa Castro3
1Institute for Systems and Computer Engineering, Technology and Science (INESC-TEC), 4200-465 Porto, Portugal.
Entropy (Basel, Switzerland)
|March 6, 2021
Summary
This review explores diverse entropy measures for time-series analysis, detailing their origins, mathematical definitions, and applications. It highlights Shannon, Tsallis, sample, permutation, and approximate entropies as most cited, crucial for selecting appropriate methods.
Area of Science:
- Entropy measures are applied across diverse scientific fields, including computer science, physics, mathematics, and engineering.
- The study focuses on time-series analysis, a common application area for various entropy variants.
Background:
- The concept of entropy, introduced by Rudolf Clausius, has evolved significantly over 160 years.
- Entropy has been extended and applied in fields such as information theory, chaos theory, data mining, and mathematical linguistics.
Purpose of the Study:
- To review and explain various entropy measures used in time-series analysis.
- To detail the emergence, mathematical definitions, relationships, and applications of different entropy variants.
- To guide researchers in selecting the most suitable entropy measure for their specific data.
Main Methods:
- A comprehensive review of entropy variants applied to time-series data.
- Analysis of citation counts over sixteen years for papers introducing new entropy measures.
- Identification of the most applied scientific fields using bibliometric data from Web of Science and Scopus.
Main Results:
- Shannon/differential, Tsallis, sample, permutation, and approximate entropies are the most frequently cited.
- Computer science, physics, mathematics, and engineering are the primary fields utilizing these entropy measures.
- The application landscape of entropy is continuously expanding with new variants and uses.
Conclusions:
- Understanding the strengths and limitations of each entropy measure is vital for advancing research.
- The selection of an appropriate entropy variant is critical for effective time-series data analysis.
- The field of entropy research is dynamic, necessitating ongoing exploration of new developments and applications.
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