翻訳と辞書 Words near each other ・ Whitemouth River Park & Campground ・ Whitemouth shiner ・ Whitemouth, Manitoba ・ Whitemud Creek ・ Whitemud Drive ・ Whitemud Formation ・ Whitemud River ・ Whiten v Pilot Insurance Co ・ Whitener Ranch ・ Whiteness ・ Whiteness (disambiguation) ・ Whiteness studies ・ Whiteness, Shetland ・ Whitenife ・ Whitening ・ Whitening transformation ・ Whitenose shark ・ Whitenose whipray ・ Whiteoak Creek Falls ・ Whiteoak Grove, West Virginia ・ Whiteoak High School ・ Whiteoak Township, Highland County, Ohio ・ Whiteochloa ・ Whiteodendron ・ Whiteout ・ Whiteout (2000 film) ・ Whiteout (2009 film) ・ Whiteout (album) ・ Whiteout (band) ・ Whiteout (comics) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Whitening transformation ： ウィキペディア英語版 Whitening transformation A whitening transformation is a decorrelation transformation that transforms an arbitrary set of variables having a known covariance matrix $M$ into a set of new variables whose covariance is the identity matrix (meaning that they are uncorrelated and all have variance 1). The transformation is called "whitening" because it changes the input vector into a white noise vector. It differs from a general decorrelation transformation in that the latter only makes the covariances equal to zero, so that the correlation matrix may be any diagonal matrix. The inverse coloring transformation transforms a vector $Y$ of uncorrelated variables (a white random vector) into a vector $X$ with a specified covariance matrix. == Definition == Suppose $X$ is a random (column) vector with covariance matrix $M$ and mean $0$. Typically (when $M$ is not singular) whitening $X$ means multiplying by $M^$. The matrix $M$ can be written as the expected value of the outer product of $X$ with itself, namely: :$M\; =\; \backslash operatorname(X^T)$ When $M$ is symmetric and positive definite (and therefore not singular), it has a positive definite symmetric square root $M^$, such that $M^M^\; =\; M$. Since $M$ is positive definite, $M^$ is invertible, and the vector $Y\; =\; M^X$ has covariance matrix: $\backslash operatorname(Y)\; =\; \backslash operatorname(Y^T)\; =\; M^\; \backslash operatorname(X^T)\; (M^)^T\; =\; M^\; M\; M^\; =\; I$ and is therefore a white random vector. If $M$ is singular (and hence not positive definite), then $M^$ is not invertible, and it is impossible to map $X$ to a white vector with the same number of components. In that case the vector $X$ can still be mapped to a smaller white vector $Y$ with $m$ elements, where $m$ is the number of non-zero eigenvalues of $M$. 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「Whitening transformation」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.