更改

Normalized variants of the mutual information are provided by the coefficients of constraint, uncertainty coefficient or proficiency:

Normalized variants of the mutual information are provided by the coefficients of constraint, uncertainty coefficient or proficiency:

互信息的规范化变量由约束系数、不确定系数或熟练程度提供:  

互信息的规范化变量由约束系数、不确定系数或熟练程度组成:  

:<math>

:<math>

C_{XY} = \frac{\operatorname{I}(X;Y)}{H(Y)}

C_{XY} = \frac{\operatorname{I}(X;Y)}{H(Y)}

~~~~\mbox{and}~~~~  

~~~~\mbox{和}~~~~  

C_{YX} = \frac{\operatorname{I}(X;Y)}{H(X)}.

C_{YX} = \frac{\operatorname{I}(X;Y)}{H(X)}.

The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following redundancy measure:

The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following redundancy measure:

这两个系数的值范围为[0,1] ，但不一定相等。在某些情况下，可能需要一个对称的度量，例如下面的冗余度量:

这两个系数的值范围均为[0,1]，但不一定是相等的。在某些情况下，可能需要一个对称的度量，例如下面的冗余度量:

:<math>R = \frac{\operatorname{I}(X;Y)}{H(X) + H(Y)}</math>

:<math>R = \frac{\operatorname{I}(X;Y)}{H(X) + H(Y)}</math>

which attains a minimum of zero when the variables are independent and a maximum value of

which attains a minimum of zero when the variables are independent and a maximum value of

Another symmetrical measure is the symmetric uncertainty , given by

Another symmetrical measure is the symmetric uncertainty , given by

If we consider mutual information as a special case of the total correlation or dual total correlation, the normalized version are respectively,

If we consider mutual information as a special case of the total correlation or dual total correlation, the normalized version are respectively,

如果我们把互信息看作是总相关或对偶总相关的特殊情况，归一化版本分别为,

如果我们把互信息看作是'''<font color="#ff8000">总相关 Total correlation</font>'''或'''<font color="#ff8000">对偶总相关 Dual total correlation</font>'''的特殊情况，则其标准化版本分别为,

:<math>\frac{\operatorname{I}(X;Y)}{\min\left[ H(X),H(Y)\right]}</math> and <math>\frac{\operatorname{I}(X;Y)}{H(X,Y)} \; .</math>

:<math>\frac{\operatorname{I}(X;Y)}{\min\left[ H(X),H(Y)\right]}</math> and <math>\frac{\operatorname{I}(X;Y)}{H(X,Y)} \; .</math>

This normalized version also known as Information Quality Ratio (IQR) which quantifies the amount of information of a variable based on another variable against total uncertainty:

This normalized version also known as Information Quality Ratio (IQR) which quantifies the amount of information of a variable based on another variable against total uncertainty:

这个标准化版本也被称为信息质量比率(IQR) ，它根据另一个变量量化了一个变量的信息量，以对抗总的不确定性:  

这个标准化版本也被称为'''<font color="#ff8000">信息质量比率 Information Quality Ratio，IQR</font>''' ，它根据另一个变量量化了一个变量的信息量，来对抗总的不确定性:  

:<math>IQR(X, Y) = \operatorname{E}[\operatorname{I}(X;Y)]  

:<math>IQR(X, Y) = \operatorname{E}[\operatorname{I}(X;Y)]  

There's a normalization which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]).  Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],

There's a normalization which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]).  Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],