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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 canonical correlation ： ウィキペディア英語版 canonical correlation In statistics, canonical-correlation analysis (CCA) is a way of making sense of cross-covariance matrices. If we have two vectors ''X'' = (''X''1, ..., ''X''''n'') and ''Y'' = (''Y''1, ..., ''Y''''m'') of random variables, and there are correlations among the variables, then canonical-correlation analysis will find linear combinations of the ''X''''i'' and ''Y''''j'' which have maximum correlation with each other. T. R. Knapp notes "virtually all of the commonly encountered parametric tests of significance can be treated as special cases of canonical-correlation analysis, which is the general procedure for investigating the relationships between two sets of variables." The method was first introduced by Harold Hotelling in 1936. ==Definition== Given two column vectors $X\; =\; (x\_1,\; \backslash dots,\; x\_n)\text{'}$ and $Y\; =\; (y\_1,\; \backslash dots,\; y\_m)\text{'}$ of random variables with finite second moments, one may define the cross-covariance $\backslash Sigma\; \_\; =\; \backslash operatorname(X,\; Y)$ to be the $n\; \backslash times\; m$ matrix whose $(i,\; j)$ entry is the covariance $\backslash operatorname(x\_i,\; y\_j)$. In practice, we would estimate the covariance matrix based on sampled data from $X$ and $Y$ (i.e. from a pair of data matrices). Canonical-correlation analysis seeks vectors $a$ and $b$ such that the random variables $a\text{'}\; X$ and $b\text{'}\; Y$ maximize the correlation $\backslash rho\; =\; \backslash operatorname(a\text{'}\; X,\; b\text{'}\; Y)$. The random variables $U\; =\; a\text{'}\; X$ and $V\; =\; b\text{'}\; Y$ are the ''first pair of canonical variables''. Then one seeks vectors maximizing the same correlation subject to the constraint that they are to be uncorrelated with the first pair of canonical variables; this gives the ''second pair of canonical variables''. This procedure may be continued up to $\backslash min\backslash$ times. 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「canonical correlation」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.