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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 Low-rank approximation ： ウィキペディア英語版 Low-rank approximation In mathematics, low-rank approximation is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constraint that the approximating matrix has reduced rank. The problem is used for mathematical modeling and data compression. The rank constraint is related to a constraint on the complexity of a model that fits the data. In applications, often there are other constraints on the approximating matrix apart from the rank constraint, e.g., non-negativity and Hankel structure. Low-rank approximation is closely related to: * principal component analysis, * factor analysis, * total least squares, * latent semantic analysis, and * orthogonal regression. == Definition == Given * structure specification $\backslash mathcal\; :\; \backslash mathbb^\; \backslash to\; \backslash mathbb^$, * vector of structure parameters $p\backslash in\backslash mathbb^$, and * desired rank $r$, :$$ \text \quad \text \widehat p \quad \|p - \widehat p\| \quad\text\quad \operatorname\big(\mathcal(\widehat p)\big) \leq r. 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「Low-rank approximation」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.