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An Optimization Approach of Deriving Bounds between Entropy and Error from Joint Distribution: Case Study for Binary Classifications
Hu, Bao-Gang1; Xing, Hong-Jie2
Source PublicationENTROPY
2016-02-01
Volume18Issue:2Pages:1-19
SubtypeArticle
AbstractIn this work, we propose a new approach of deriving the bounds between entropy and error from a joint distribution through an optimization means. The specific case study is given on binary classifications. Two basic types of classification errors are investigated, namely, the Bayesian and non-Bayesian errors. The consideration of non-Bayesian errors is due to the facts that most classifiers result in non-Bayesian solutions. For both types of errors, we derive the closed-form relations between each bound and error components. When Fano's lower bound in a diagram of Error Probability vs. Conditional Entropy is realized based on the approach, its interpretations are enlarged by including non-Bayesian errors and the two situations along with independent properties of the variables. A new upper bound for the Bayesian error is derived with respect to the minimum prior probability, which is generally tighter than Kovalevskij's upper bound.
KeywordEntropy Error Probability Bayesian Errors Error Types Upper Bound Lower Bound
WOS HeadingsScience & Technology ; Physical Sciences
DOI10.3390/e18020059
WOS KeywordPATTERN-RECOGNITION ; FEATURE-SELECTION ; PROBABILITY ; INFORMATION ; INEQUALITIES ; DECISIONS ; CRITERIA
Indexed BySCI
Language英语
Funding OrganizationNational Natural Science Foundation of China(61273196 ; 61573348 ; 60903089)
WOS Research AreaPhysics
WOS SubjectPhysics, Multidisciplinary
WOS IDWOS:000371827800018
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Document Type期刊论文
Identifierhttp://ir.ia.ac.cn/handle/173211/11372
Collection模式识别国家重点实验室_多媒体计算与图形学
Affiliation1.Chinese Acad Sci, Inst Automat, NLPR LIAMA, Beijing 100190, Peoples R China
2.Hebei Univ, Coll Math & Informat Sci, Baoding 071002, Peoples R China
Recommended Citation
GB/T 7714
Hu, Bao-Gang,Xing, Hong-Jie. An Optimization Approach of Deriving Bounds between Entropy and Error from Joint Distribution: Case Study for Binary Classifications[J]. ENTROPY,2016,18(2):1-19.
APA Hu, Bao-Gang,&Xing, Hong-Jie.(2016).An Optimization Approach of Deriving Bounds between Entropy and Error from Joint Distribution: Case Study for Binary Classifications.ENTROPY,18(2),1-19.
MLA Hu, Bao-Gang,et al."An Optimization Approach of Deriving Bounds between Entropy and Error from Joint Distribution: Case Study for Binary Classifications".ENTROPY 18.2(2016):1-19.
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