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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 Tversky index ： ウィキペディア英語版 Tversky index The Tversky index, named after Amos Tversky, is an asymmetric similarity measure on sets that compares a variant to a prototype. The Tversky index can be seen as a generalization of Dice's coefficient and Tanimoto coefficient. For sets ''X'' and ''Y'' the Tversky index is a number between 0 and 1 given by $S(X,\; Y)\; =\; \backslash frac$, Here, $X\; -\; Y$ denotes the relative complement of Y in X. Further, $\backslash alpha,\; \backslash beta\; \backslash ge\; 0$ are parameters of the Tversky index. Setting $\backslash alpha\; =\; \backslash beta\; =\; 1$ produces the Tanimoto coefficient; setting $\backslash alpha\; =\; \backslash beta\; =\; 0.5$ produces Dice's coefficient. If we consider ''X'' to be the prototype and ''Y'' to be the variant, then $\backslash alpha$ corresponds to the weight of the prototype and $\backslash beta$ corresponds to the weight of the variant. Tversky measures with $\backslash alpha\; +\; \backslash beta\; =\; 1$ are of special interest.〔http://www.daylight.com/dayhtml/doc/theory/theory.finger.html〕 Because of the inherent asymmetry, the Tversky index does not meet the criteria for a similarity metric. However, if symmetry is needed a variant of the original formulation has been proposed using max and min functions 〔Jimenez, S., Becerra, C., Gelbukh, A. (SOFTCARDINALITY-CORE: Improving Text Overlap with Distributional Measures for Semantic Textual Similarity ). Second Joint Conference on Lexical and Computational Semantics ( *SEM), Volume 1: Proceedings of the Main Conference and the Shared Task: Semantic Textual Similarity, p.194-201, June 7–8, 2013, Atlanta, Georgia, USA.〕 . $S(X,Y)=\backslash frac$, $a=\backslash min\backslash left(|X-Y|,|Y-X|\backslash right)$, $b=\backslash max\backslash left(|X-Y|,|Y-X|\backslash right)$, This formulation also re-arranges parameters $\backslash alpha$ and $\backslash beta$. Thus, $\backslash alpha$ controls the balance between $|X\; -\; Y|$ and $|Y\; -\; X|$ in the denominator. Similarly, $\backslash beta$ controls the effect of the symmetric difference $|X\backslash ,\backslash triangle\backslash ,Y\backslash ,|$ versus $|\; X\; \backslash cap\; Y\; |$ in the denominator. ==Notes== 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「Tversky index」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.