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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 Kendall tau distance ： ウィキペディア英語版 Kendall tau distance The Kendall tau rank distance is a metric that counts the number of pairwise disagreements between two ranking lists. The larger the distance, the more dissimilar the two lists are. Kendall tau distance is also called bubble-sort distance since it is equivalent to the number of swaps that the bubble sort algorithm would make to place one list in the same order as the other list. The Kendall tau distance was created by Maurice Kendall. ==Definition== The Kendall tau ranking distance between two lists $L1$ and $L2$ is : $K(\backslash tau\_1,\backslash tau\_2)\; =\; |\backslash |.$ where * $\backslash tau\_1(i)$ and $\backslash tau\_2(i)$ are the rankings of the element i in $L1$ and $L2$ respectively. $K(\backslash tau\_1,\backslash tau\_2)$ will be equal to 0 if the two lists are identical and $n(n-1)/2$ (where $n$ is the list size) if one list is the reverse of the other. Often Kendall tau distance is normalized by dividing by $n(n-1)/2$ so a value of 1 indicates maximum disagreement. The normalized Kendall tau distance therefore lies in the interval (). Kendall tau distance may also be defined as : $K(\backslash tau\_1,\backslash tau\_2)\; =\; \backslash begin\; \backslash sum\_\; \backslash bar\_(\backslash tau\_1,\backslash tau\_2)\; \backslash end$ where * ''P'' is the set of unordered pairs of distinct elements in $\backslash tau\_1$ and $\backslash tau\_2$ * $\backslash bar\_(\backslash tau\_1,\backslash tau\_2)$ = 0 if ''i'' and ''j'' are in the same order in $\backslash tau\_1$ and $\backslash tau\_2$ * $\backslash bar\_(\backslash tau\_1,\backslash tau\_2)$ = 1 if ''i'' and ''j'' are in the opposite order in $\backslash tau\_1$ and $\backslash tau\_2.$ Kendall tau distance can also be defined as the total number of discordant pairs. Kendall tau distance in Rankings: A permutation (or ranking) is an array of N integers where each of the integers between 0 and N-1 appears exactly once. The Kendall tau distance between two rankings is the number of pairs that are in different order in the two rankings. For example the Kendall tau distance between 0 3 1 6 2 5 4 and 1 0 3 6 4 2 5 is four because the pairs 0-1, 3-1, 2-4, 5-4 are in different order in the two rankings, but all other pairs are in the same order.〔http://algs4.cs.princeton.edu/25applications/〕 If Kendall tau function is performed as $K(L1,L2)$ instead of $K(\backslash tau\_1,\backslash tau\_2)$ (where $\backslash tau\_1$ and $\backslash tau\_2$ are the rankings of $L1$ and $L2$ elements respectively), then triangular inequality is not guaranteed. The triangular inequality fail in cases where there are repetitions in the lists. So then we are not any more dealing with a metric. 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「Kendall tau distance」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.