On defining partition entropy by inequalities

doi:10.1109/TIT.2007.903124

	On defining partition entropy by inequalities
	Luo, Ping ; Zhan, Guoxing ; He, Qing ; Shi, Zhongzhi ; Lue, Kevin
	2007-09-01
发表期刊	IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN	0018-9448
卷号	53 期号:9 页码:3233-3239
摘要	Partition entropy is the numerical metric of uncertainty within a partition of a finite set, while conditional entropy measures the degree of difficulty in predicting a decision partition when a condition partition is provided. Since two direct methods exist for defining conditional entropy based on its partition entropy, the inequality postulates of monotonicity, which conditional entropy satisfies, are actually additional constraints on its entropy. Thus, in this paper partition entropy is defined as a function of probability distribution, satisfying all the inequalities of not only partition entropy itself but also its conditional counterpart. These inequality postulates formalize the intuitive understandings of uncertainty contained in partitions of finite sets. We study the relationships between these inequalities, and reduce the redundancies among them. According to two different definitions of conditional entropy from its partition entropy, the convenient and unified checking conditions for any partition entropy are presented, respectively. These properties generalize and illuminate the common nature of all partition entropies.
关键词	conditional entropy inequality partition entropy uncertainty
DOI	10.1109/TIT.2007.903124
收录类别	SCI
语种	英语
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Information Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000249025100022
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计	被引频次：9[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://119.78.100.204/handle/2XEOYT63/10829
专题	中国科学院计算技术研究所期刊论文_英文
通讯作者	Luo, Ping
作者单位	1.Chinese Acad Sci, Inst Comp Technol, Key Lab Intelligent Informat Proc, Beijing 100080, Peoples R China 2.Chinese Acad Sci, Grad Univ, Beijing 100864, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 4.Brunel Univ, Uxbridge UB8 3PH, Middx, England
推荐引用方式 GB/T 7714	Luo, Ping,Zhan, Guoxing,He, Qing,et al. On defining partition entropy by inequalities[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,2007,53(9):3233-3239.
APA	Luo, Ping,Zhan, Guoxing,He, Qing,Shi, Zhongzhi,&Lue, Kevin.(2007).On defining partition entropy by inequalities.IEEE TRANSACTIONS ON INFORMATION THEORY,53(9),3233-3239.
MLA	Luo, Ping,et al."On defining partition entropy by inequalities".IEEE TRANSACTIONS ON INFORMATION THEORY 53.9(2007):3233-3239.