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第361行：
第361行： − + 第367行：
第367行： − 许多应用程序需要一个度量单位，即两个点之间的距离度量单位。数量+ − 第392行：
第391行： − 满足度量的性质(三角不等式、非负性、不可分性和对称性)。这个距离度量也称为信息的变化。+ − − − If <math>X, Y</math> are discrete random variables then all the entropy terms are non-negative, so <math>0 \le d(X,Y) \le H(X,Y)</math> and one can define a normalized distance − 如果数学 x，y / math 是离散随机变量，那么所有的熵项都是非负的，所以数学0 le d (x，y) le Eta (x，y) / math 可以定义一个标准化距离+ − + 第415行：
第411行： − + − − 数学公制 d / math 是一个通用的公制，因为如果任何其他距离公制把数学 x / math 和数学 y / math 放在附近，那么数学公制 d / math 也会把它们放在附近。 + 第427行：
第422行： − 插入定义表明+ 第441行：
第436行： − + − − 在对信息的集合论解释中(见条件熵图) ，这实际上是数学 x / 数学和数学 y / 数学之间的雅可比相似度系数。 + 第464行：
第458行： − 也是一个度量标准。+
→公制 Metric
=== 公制 Metric ===
=== 度量 Metric ===
Many applications require a [[metric (mathematics)|metric]], that is, a distance measure between pairs of points. The quantity
Many applications require a [[metric (mathematics)|metric]], that is, a distance measure between pairs of points. The quantity
Many applications require a metric, that is, a distance measure between pairs of points. The quantity
Many applications require a metric, that is, a distance measure between pairs of points. The quantity
许多应用需要一个度量，即点对之间的距离度量。这个量：
satisfies the properties of a metric (triangle inequality, non-negativity, indiscernability and symmetry). This distance metric is also known as the variation of information.
satisfies the properties of a metric (triangle inequality, non-negativity, indiscernability and symmetry). This distance metric is also known as the variation of information.
满足度量的性质（三角形不等式、非负性、不可除性和对称性）。这种距离度量也称为信息的变化。
If <math>X, Y</math> are discrete random variables then all the entropy terms are non-negative, so <math>0 \le d(X,Y) \le H(X,Y)</math> and one can define a normalized distance
If <math>X, Y</math> are discrete random variables then all the entropy terms are non-negative, so <math>0 \le d(X,Y) \le H(X,Y)</math> and one can define a normalized distance
If 𝑋,𝑌 are discrete random variables then all the entropy terms are non-negative, so 0≤𝑑(𝑋,𝑌)≤𝐻(𝑋,𝑌) and one can define a normalized distance
如果𝑋，𝑌是离散随机变量，那么所有熵项都是非负的，因此0≤𝑑（𝑋，𝑌）≤𝐻（𝑋，𝑌），可以定义一个标准化距离：
The metric <math>D</math> is a universal metric, in that if any other distance measure places <math>X</math> and <math>Y</math> close-by, then the <math>D</math> will also judge them close.<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref>{{dubious|see talk page|date=November 2014}}
The metric <math>D</math> is a universal metric, in that if any other distance measure places <math>X</math> and <math>Y</math> close-by, then the <math>D</math> will also judge them close.<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref>{{dubious|see talk page|date=November 2014}}
The metric <math>D</math> is a universal metric, in that if any other distance measure places <math>X</math> and <math>Y</math> close-by, then the <math>D</math> will also judge them close.
The metric 𝐷 is a universal metric, in that if any other distance measure places 𝑋 and 𝑌 close-by, then the 𝐷 will also judge them close.
度量𝐷是一种通用度量，即如果任何其他距离度量将𝑋和𝑌放在附近，则𝐷也将判断它们接近。
Plugging in the definitions shows that
Plugging in the definitions shows that
从如下定义可以看出：
In a set-theoretic interpretation of information (see the figure for [[Conditional entropy]]), this is effectively the [[Jaccard index|Jaccard distance]] between <math>X</math> and <math>Y</math>.
In a set-theoretic interpretation of information (see the figure for [[Conditional entropy]]), this is effectively the [[Jaccard index|Jaccard distance]] between <math>X</math> and <math>Y</math>.
In a set-theoretic interpretation of information (see the figure for Conditional entropy), this is effectively the Jaccard distance between <math>X</math> and <math>Y</math>.
In a set-theoretic interpretation of information (see the figure for Conditional entropy), this is effectively the Jaccard distance between 𝑋 and 𝑌.
在信息的集合论解释中（参见条件熵的图），这实际上就是𝑋和𝑌之间的Jaccard距离。
is also a metric.
is also a metric.
也是一种度量标准。
=== 条件互信息 Conditional mutual information ===
=== 条件互信息 Conditional mutual information ===