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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 Two-dimensional singular value decomposition ： ウィキペディア英語版 Two-dimensional singular value decomposition Two-dimensional singular value decomposition (2DSVD) computes the low-rank approximation of a set of matrices such as 2D images or weather maps in a manner almost identical to SVD (singular value decomposition) which computes the low-rank approximation of a single matrix (or a set of 1D vectors). ==SVD== Let matrix $X=(x\_1,...,x\_n)$ contains the set of 1D vectors which have been centered. In PCA/SVD, we construct covariance matrix $F$ and Gram matrix $G$ : $F=X\; X^T$ , $G=X^T\; X$, and compute their eigenvectors $U\; =\; (u\_1,\; ...,\; u\_n)$ and $V=(v\_1,...,\; v\_n)$. Since $VV^T=I,\; UU^T=I$, we have : $X\; =\; UU^T\; X\; VV^T\; =\; U\; (U^T\; XV)\; V^T\; =\; U\; \backslash Sigma\; V^T$ If we retain only $K$ principal eigenvectors in $U\; ,\; V$, this gives low-rank approximation of $X$. 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「Two-dimensional singular value decomposition」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.