Jensen–Shannon divergence

最新推荐文章于 2024-12-26 21:29:17 发布

DreaMaker丶

最新推荐文章于 2024-12-26 21:29:17 发布

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Jensen–Shannon divergence（J-S散度） is a method of measuring the similarity between two probability distributions.

It is based on the Kullback–Leibler divergence（K-L散度）, with some notable

(and useful) differences, including that it is symmetric and it is always a finite value.

The Jensen–Shannon divergence (JSD) $M_{+}^{1}(A)\times M_{+}^{1}(A)\rightarrow [0,\infty {})$ is a symmetrized and smoothed version of the Kullback–Leibler divergence $D(P\parallel Q)$ . It is defined by：

${{\rm {JSD}}}(P\parallel Q)={\frac {1}{2}}D(P\parallel M)+{\frac {1}{2}}D(Q\parallel M)$ where $M={\frac {1}{2}}(P+Q)$

The Jensen–Shannon divergence is bounded by 1 for two probability distributions, given that one uses the base 2 logarithm. $0\leq {{\rm {JSD}}}(P\parallel Q)\leq 1$

For log base e, or ln, which is commonly used in statistical thermodynamics, the upper bound is ln(2): $0\leq {{\rm {JSD}}}(P\parallel Q)\leq \ln(2)$

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