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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Information radius ： ウィキペディア英語版 Jensen–Shannon divergence In probability theory and statistics, the Jensen–Shannon divergence is a popular method of measuring the similarity between two probability distributions. It is also known as information radius (IRad) or total divergence to the average. It is based on the Kullback–Leibler divergence, with some notable (and useful) differences, including that it is symmetric and it is always a finite value. The square root of the Jensen–Shannon divergence is a metric often referred to as Jensen-Shannon distance. ==Definition== Consider the set $M\_+^1(A)$ of probability distributions where A is a set provided with some σ-algebra of measurable subsets. In particular we can take A to be a finite or countable set with all subsets being measurable. The Jensen–Shannon divergence (JSD) $M\_+^1(A)\; \backslash times\; M\_+^1(A)\; \backslash rightarrow\; [0,\backslash inftyD(P\; \backslash parallel\; M)+\backslash fracD(Q\; \backslash parallel\; M)$ where $M=\backslash frac(P+Q)$ A more general definition, allowing for the comparison of more than two probability distributions, is: :$\_(P\_1,\; P\_2,\; \backslash ldots,\; P\_n)\; =\; H\backslash left(\backslash sum\_^n\; \backslash pi\_i\; P\_i\backslash right)\; -\; \backslash sum\_^n\; \backslash pi\_i\; H(P\_i)$ where $\backslash pi\_1,\; \backslash ldots,\; \backslash pi\_n$ are weights that are selected for the probability distributions $P\_1,\; P\_2,\; \backslash ldots,\; P\_n$ and $H(P)$ is the Shannon entropy for distribution $P$. For the two-distribution case described above, :$P\_1=P,\; P\_2=Q,\; \backslash pi\_1\; =\; \backslash pi\_2\; =\; \backslash frac.\backslash$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Jensen–Shannon divergence」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.