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Entropy 2017, 19(6), 269; doi:10.3390/e19060269

A Novel Distance Metric: Generalized Relative Entropy

1,2,* , 1,2
,
1,2
and
1,2
1
College of Computer Science, Inner Mongolia University, Hohhot 010010, China
2
Inner Mongolia Key Laboratory of Data Mining and Knowledge Engineering, Hohhot 010010, China
*
Author to whom correspondence should be addressed.
Received: 26 May 2017 / Revised: 7 June 2017 / Accepted: 7 June 2017 / Published: 13 June 2017
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory III)
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Abstract

Information entropy and its extension, which are important generalizations of entropy, are currently applied to many research domains. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional relative entropy. We present the structure of generalized relative entropy after the discussion of defects in relative entropy. Moreover, some properties of the provided generalized relative entropy are presented and proved. The provided generalized relative entropy is proved to have a finite range and is a finite distance metric. Finally, we predict nucleosome positioning of fly and yeast based on generalized relative entropy and relative entropy respectively. The experimental results show that the properties of generalized relative entropy are better than relative entropy. View Full-Text
Keywords: relative entropy; generalized relative entropy; upper bound; distance metric; adjusted distance relative entropy; generalized relative entropy; upper bound; distance metric; adjusted distance
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Liu, S.; Lu, M.; Liu, G.; Pan, Z. A Novel Distance Metric: Generalized Relative Entropy. Entropy 2017, 19, 269.

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