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Entropy 2017, 19(6), 260; doi:10.3390/e19060260

Information Distances versus Entropy Metric

1
,
2,3
and
3,*
1
School of Mechanical and Electrical Engineering, Guizhou Normal University, Guiyang 550025, China
2
School of Electronics and Communication Engineering, Yulin Normal University, Yulin 537000, China
3
School of Information Science and Engineering, Xiamen University, Xiamen 361005, China
*
Author to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 18 April 2017 / Revised: 2 June 2017 / Accepted: 2 June 2017 / Published: 7 June 2017
(This article belongs to the Section Information Theory)
View Full-Text   |   Download PDF [222 KB, uploaded 7 June 2017]

Abstract

Information distance has become an important tool in a wide variety of applications. Various types of information distance have been made over the years. These information distance measures are different from entropy metric, as the former is based on Kolmogorov complexity and the latter on Shannon entropy. However, for any computable probability distributions, up to a constant, the expected value of Kolmogorov complexity equals the Shannon entropy. We study the similar relationship between entropy and information distance. We also study the relationship between entropy and the normalized versions of information distances. View Full-Text
Keywords: entropy; Kolmogorov complexity; information distance; normalized information distance entropy; Kolmogorov complexity; information distance; normalized information distance
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Hu, B.; Bi, L.; Dai, S. Information Distances versus Entropy Metric. Entropy 2017, 19, 260.

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