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Applications of Entropy in Data Analysis and Machine Learning: A Review
Salomé A Sepúlveda-Fontaine1, José M Amigó1
1Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, 03202 Elche, Spain.
Entropy (Basel, Switzerland)
|January 8, 2025
Summary
Entropy, a concept from thermodynamics, is crucial in data analysis and machine learning for characterizing probability distributions. This review highlights diverse entropy applications, demonstrating its power and versatility in these fields.
Area of Science:
- Information Theory
- Statistical Mechanics
- Machine Learning
- Data Analysis
Background:
- Entropy originated in 19th-century thermodynamics and expanded into physics and mathematics.
- Classical entropies include Boltzmann-Gibbs, von Neumann, Shannon, Kolmogorov-Sinai, and topological entropies.
- Numerous entropy variations have been developed for specific applications.
Purpose of the Study:
- To review the applications of various entropy measures in data analysis and machine learning.
- To focus on entropies that characterize probability mass distributions.
- To provide an axiomatic characterization of entropies based on Shannon and Khinchin.
Main Methods:
- Reviewing classical and contemporary entropy measures.
- Selecting a representative group of entropies for discussion.
- Focusing on entropies defined as positive functionals on probability mass distributions.
- Utilizing an axiomatic characterization tracing back to Shannon and Khinchin.
Main Results:
- Entropies are highly effective for characterizing probability mass distributions.
- The review showcases diverse applications of entropy in data analysis and machine learning.
- Classical and novel entropy measures demonstrate significant utility.
Conclusions:
- Entropy is a powerful and versatile concept with broad applications in data analysis and machine learning.
- Entropies provide a robust framework for understanding and analyzing probability distributions.
- The continued development and application of entropy measures are vital for advancing these fields.
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