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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 Linear separability ： ウィキペディア英語版 Linear separability In Euclidean geometry, linear separability is a geometric property of a pair of sets of points. This is most easily visualized in two dimensions (the Euclidean plane) by thinking of one set of points as being colored blue and the other set of points as being colored red. These two sets are ''linearly separable'' if there exists at least one line in the plane with all of the blue points on one side of the line and all the red points on the other side. This idea immediately generalizes to higher-dimensional Euclidean spaces if line is replaced by hyperplane. The problem of determining if a pair of sets is linearly separable and finding a separating hyperplane if they are arises in several areas. In statistics and machine learning, classifying certain types of data is a problem for which good algorithms exist that are based on this concept. ==Mathematical definition== Let $X\_$ and $X\_$ be two sets of points in an ''n''-dimensional Euclidean space. Then $X\_$ and $X\_$ are ''linearly separable'' if there exists ''n'' + 1 real numbers $w\_,\; w\_,..,w\_,\; k$, such that every point $x\; \backslash in\; X\_$ satisfies $\backslash sum^\_\; w\_x\_\; >\; k$ and every point $x\; \backslash in\; X\_$ satisfies , where $x\_$ is the $i$-th component of $x$. Equivalently, two sets are linearly separable precisely when their respective convex hulls are disjoint (colloquially, do not overlap). 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「Linear separability」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.