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The concept of shattered sets plays an important role in Vapnik–Chervonenkis theory, also known as VC-theory. Shattering and VC-theory are used in the study of empirical processes as well as in statistical computational learning theory. ==Definition== Suppose we have a class ''C'' of sets and a given set ''A''. ''C'' is said to ''shatter'' ''A'' if, for each subset ''T'' of ''A'', there is some element ''U'' of ''C'' such that : Equivalently, ''C'' shatters ''A'' when the power set ''P''(''A'') = . For example, the class ''C'' of all discs in the plane (two-dimensional space) cannot shatter every set ''A'' of four points, yet the class of all convex sets in the plane shatters every finite set on the (unit) circle. (For the latter result, connect the dots!) We employ the letter ''C'' to refer to a "class" or "collection" of sets, as in a Vapnik–Chervonenkis class (VC-class). The set ''A'' is often assumed to be finite because, in empirical processes, we are interested in the shattering of finite sets of data points. 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「Shattered set」の詳細全文を読む スポンサード リンク
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