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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 optimal matching ： ウィキペディア英語版 optimal matching Optimal matching is a sequence analysis method used in social science, to assess the dissimilarity of ordered arrays of tokens that usually represent a time-ordered sequence of socio-economic states two individuals have experienced. Once such distances have been calculated for a set of observations (e.g. individuals in a cohort) classical tools (such as cluster analysis) can be used. The method was tailored to social sciences〔A. Abbott and A. Tsay, (2000) ''(Sequence Analysis and Optimal Matching Methods in Sociology: Review and Prospect )'' Sociological Methods & Research], Vol. 29, 3-33. 〕 from a technique originally introduced to study molecular biology (protein or genetic) sequences (see sequence alignment). Optimal matching uses the Needleman-Wunsch algorithm. == Algorithm == Let $S\; =\; (s\_1,\; s\_2,\; s\_3,\; \backslash ldots\; s\_T)$ be a sequence of states $s\_i$ belonging to a finite set of possible states. Let us denote $$ the sequence space, i.e. the set of all possible sequences of states. Optimal matching algorithms work by defining simple operator algebras that manipulate sequences, i.e. a set of operators $a\_i:\; \backslash rightarrow$. In the most simple approach, a set composed of only three basic operations to transform sequences is used: * one state $s$ is inserted in the sequence $a^\_\; (s\_1,\; s\_2,\; s\_3,\; \backslash ldots\; s\_T)\; =\; (s\_1,\; s\_2,\; s\_3,\; \backslash ldots,\; s\text{'},\; \backslash ldots\; s\_T)$ * one state is deleted from the sequence $a^\_\; (s\_1,\; s\_2,\; s\_3,\; \backslash ldots\; s\_T)\; =\; (s\_1,\; s\_3,\; \backslash ldots\; s\_T)$ and * a state $s\_1$ is replaced (substituted) by state $s\text{'}\_1$, $a^\_\; (s\_1,\; s\_2,\; s\_3,\; \backslash ldots\; s\_T)\; =\; (s\text{'}\_1,\; s\_2,\; s\_3,\; \backslash ldots\; s\_T)$. Imagine now that a ''cost'' $c(a\_i)\; \backslash in\; ^+\_0$ is associated to each operator. Given two sequences $S\_1$ and $S\_2$, the idea is to measure the ''cost'' of obtaining $S\_2$ from $S\_1$ using operators from the algebra. Let $A=$ be a sequence of operators such that the application of all the operators of this sequence $A$ to the first sequence $S\_1$ gives the second sequence $S\_2$: $S\_2\; =\; a\_1\; \backslash circ\; a\_2\; \backslash circ\; \backslash ldots\; \backslash circ\; a\_\; (S\_1)$ where $a\_1\; \backslash circ\; a\_2$ denotes the compound operator. To this set we associate the cost $c(A)\; =\; \backslash sum\_^n\; c(a\_i)$, that represents the total cost of the transformation. One should consider at this point that there might exist different such sequences $A$ that transform $S\_1$ into $S\_2$; a reasonable choice is to select the cheapest of such sequences. We thus call distance $d(S\_1,S\_2)=\; \backslash min\_A\; \backslash left\; \backslash$ that is, the cost of the least expensive set of transformations that turn $S\_1$ into $S\_2$. Notice that $d(S\_1,S\_2)$ is by definition nonnegative since it is the sum of positive costs, and trivially $d(S\_1,S\_2)=0$ if and only if $S\_1=S\_2$, that is there is no cost. The distance function is symmetric if insertion and deletion costs are equal $c(a^)\; =\; c(a^)$; the term ''indel'' cost usually refers to the common cost of insertion and deletion. Considering a set composed of only the three basic operations described above, this proximity measure satisfies the triangular inequality. Transitivity however, depends on the definition of the set of elementary operations. 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「optimal matching」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.