An algebraic approach to entropy and its generalizations: a survey

  • Authors:
  • Dan A. Simovici

  • Affiliations:
  • Univ. of Massachusetts Boston, Dept. of Computer Science, Boston

  • Venue:
  • Beyond two
  • Year:
  • 2003

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Abstract

We discuss several axiomatizations of entropy and some of its generalizations using an algebraic approach. The entropy is defined for such objects as functions, partitions, and set collections and the axiomatizations use natural operations on such objects. The generalizations of entropy we propose have applications in circuit design, data mining, machine learning, and information retrieval.