一种非线性新相关信息熵定义及其性质、应用

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

在研究了相关信息熵和H_(Pal)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.

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 H_（Pal） 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.