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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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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
PubMed
Summary
This summary is machine-generated.

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.

Keywords:
data analysisdeep learningentropic measuresentropymachine learning

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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.