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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 Minkowski distance ： ウィキペディア英語版 Minkowski distance The Minkowski distance is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance. ==Definition== The Minkowski distance of order ''p'' between two points : $X=(x\_1,x\_2,\backslash ldots,x\_n)\backslash textY=(y\_1,y\_2,\backslash ldots,y\_n)\; \backslash in\; \backslash mathbb^n$ is defined as: :$\backslash left(\backslash sum\_^n\; |x\_i-y\_i|^p\backslash right)^$ For $p\backslash geq1$, the Minkowski distance is a metric as a result of the Minkowski inequality. When , the distance between (0,0) and (1,1) is $2^>2$, but the point (0,1) is at a distance 1 from both of these points. Since this violates the triangle inequality, for it is not a metric. Minkowski distance is typically used with ''p'' being 1 or 2. The latter is the Euclidean distance, while the former is sometimes known as the Manhattan distance. In the limiting case of ''p'' reaching infinity, we obtain the Chebyshev distance: :$\backslash lim\_\}\; =\; \backslash max\_^n\; |x\_i-y\_i|.\; \backslash ,$ Similarly, for ''p'' reaching negative infinity, we have: :$\backslash lim\_\}\; =\; \backslash min\_^n\; |x\_i-y\_i|.\; \backslash ,$ The Minkowski distance can also be viewed as a multiple of the power mean of the component-wise differences between ''P'' and ''Q''. The following figure shows unit circles with various values of ''p'': 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「Minkowski distance」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.