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→Information theory 信息论
In information theory and statistics, negentropy is used as a measure of distance to normality. Out of all distributions with a given mean and variance, the normal or Gaussian distribution is the one with the highest entropy. Negentropy measures the difference in entropy between a given distribution and the Gaussian distribution with the same mean and variance. Thus, negentropy is always nonnegative, is invariant by any linear invertible change of coordinates, and vanishes if and only if the signal is Gaussian.
In information theory and statistics, negentropy is used as a measure of distance to normality. Out of all distributions with a given mean and variance, the normal or Gaussian distribution is the one with the highest entropy. Negentropy measures the difference in entropy between a given distribution and the Gaussian distribution with the same mean and variance. Thus, negentropy is always nonnegative, is invariant by any linear invertible change of coordinates, and vanishes if and only if the signal is Gaussian.
在信息论和统计学中，负熵被用来度量到正态分布的距离。在所有具有给定均值和方差的分布中，正态分布或高斯分布的熵最大。负熵用来度量具有相同均值和方差的给定分布和正态分布之间熵的差距。因此，负熵总是非负的，在任何线性可逆的坐标变换下都是不变的，当且仅当信号是<font color="#ff8000">高斯分布 Gaussian distribution</font>时才变为零。
Negentropy is used in statistics and signal processing. It is related to network entropy, which is used in independent component analysis.
Negentropy is used in statistics and signal processing. It is related to network entropy, which is used in independent component analysis.
负熵通常用于统计和信号处理。它与网络熵有关，网络熵被用于<font color="#ff8000">独立成分分析 independent component analysis</font>。
The negentropy of a distribution is equal to the Kullback–Leibler divergence between <math>p_x</math> and a Gaussian distribution with the same mean and variance as <math>p_x</math> (see Differential entropy#Maximization in the normal distribution for a proof). In particular, it is always nonnegative.
The negentropy of a distribution is equal to the Kullback–Leibler divergence between <math>p_x</math> and a Gaussian distribution with the same mean and variance as <math>p_x</math> (see Differential entropy#Maximization in the normal distribution for a proof). In particular, it is always nonnegative.
一个分布的负熵等于 <math>p_x</math> 和与 <math>p_x</math> 具有与它相同均值和方差的正态分布的 Kullback-Leibler 散度(参见正态分布的<font color="#ff8000">微分熵 Differential entropy</font>和最大化)。特别地，负熵总是非负的。
一个分布的负熵等于 <math>p_x</math> 和与 <math>p_x</math> 具有相同均值和方差的正态分布的 Kullback-Leibler 散度(参见正态分布的<font color="#ff8000">微分熵 Differential entropy</font>和最大化)。特别是，它总是非负的。