一种非线性新相关信息熵定义及其性质、应用

李爱国, 汪保男

李爱国, 汪保男. 一种非线性新相关信息熵定义及其性质、应用[J]. 信息与控制, 2011, 40(3): 401-407,412.
引用本文: 李爱国, 汪保男. 一种非线性新相关信息熵定义及其性质、应用[J]. 信息与控制, 2011, 40(3): 401-407,412.
LI Aiguo, WANG Baonan. The Concept of a New Nonlinear Correlation Information Entropy and Its Properties and Applications[J]. INFORMATION AND CONTROL, 2011, 40(3): 401-407,412.
Citation: LI Aiguo, WANG Baonan. The Concept of a New Nonlinear Correlation Information Entropy and Its Properties and Applications[J]. INFORMATION AND CONTROL, 2011, 40(3): 401-407,412.

一种非线性新相关信息熵定义及其性质、应用

基金项目: 陕西省科技攻关项目(2008K01-58);陕西省教育厅自然科学专项计划资助项目(07JK314)
详细信息
    作者简介:

    李爱国(1966- ),男,博士,教授.研究领域为机器学习与数据挖掘,信息融合,软件测试.
    汪保男(1984- ),男,硕士.研究领域为数据挖掘,信息融合.

    通讯作者:

    李爱国, li_ag@sina.com

  • 中图分类号: TP271+.62

The Concept of a New Nonlinear Correlation Information Entropy and Its Properties and Applications

  • 摘要: 在研究了相关信息熵和HPal熵的基础上,提出一种以特征值代替事件发生的概率且以e为底的指数函数形式的改进的非线性新相关信息熵概念.在对有限集最大划分的条件下,推导并从理论上证明了该信息熵的若干性质,这些性质满足香农熵的基本性质.新相关信息熵是一种度量多变量、非线性系统的相关性程度大小的标准.作为多变量之间相关关系的不确定性度量,变量间的相关程度越大,对应的新相关信息熵值越小.新相关信息熵的提出有助于信息融合并为相关分析理论的研究提供了一种新方法和新思路.新相关信息熵和相关信息熵的应用实例结果对比说明新相关信息熵是一种有效且有用的度量非线性系统不确定性的方法.
    Abstract: The concept of a new nonlinear correlation information entropy(NNCIE),which uses eigenvalue to replace event probability and the function form is an exponential form whose base is e,is proposed based on the study of correlation information entropy(CIE) and HPal entropy.Under the condition of the largest partition of finite sets,some properties of this information entropy are derived and proved theoretically and these properties meet the basic properties of the information entropy proposed by Shannon.The NNCIE is a measurement criterion of multi-variable and nonlinear system's correlation degree.As an uncertainty measurement of multi-variable correlation,the more correlation information between variables is contained,the smaller value of corresponding NNCIE is.The NNCIE contributes to information fusion and provides a new method and idea for the research of correlation analysis theory.The results of contrast between NNCIE and CIE show that NNCIE is an effective and useful measurement method of nonlinear system's uncertainty.
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出版历程
  • 收稿日期:  2010-03-22
  • 发布日期:  2011-06-19

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