Correlation Degree and Correlation Coefficient of Multi-Output Functions

摘要

We present definitions of the correlation degree and correlation coefficient of multi-output functions. Two relationships about the correlation degree of multi-output functions are proved. One is between the correlation degree and independency, the other is between the correlation degree and balance. Especially the paper discusses the correlation degree of affine multi-output functions. We demonstrate properties of the correlation coefficient of multi-output functions. One is the value range of the correlation coefficient, one is the relationship between the correlation coefficient and independency, and another is the sufficient and necessary condition that two multi-output functions are equivalent to each other.