The Correlation Measures And The Improvement Of Clustering For Variables

This paper analysis the correlations of random variables: simple correlation, multiple correlations, canonical correlation and generalized correlation. Hey only can identify linear correlation between two variables but can not thoroughly explain the inner relation of variables more than two. In 1959 S. Kullback introduced the discriminant function to evaluate the likelihood of two distributions consequently portrays the inner relation of random variables. Unlike the former correlation coefficent, the value of discriminant function can be infinite, it can be more specific and it is an inner correlation, can be nonlinear.This article uses discriminant function to portray the independence of two random variables and gained the inner relations of a random vector by Hadamard inequality and improved the classification analysis for index. Here, we solved those two problems: first, technically we used penalty factor; second, theoretically with this improved classified method we proved the monotonity of merging distance.As to the application, we use this improved classifying method in classifying the survey on the lower reaches of Tarim River in 2005 - 2006. Compared with former method, this classificaton result is more specific and accurate.