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

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.