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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 correlation integral ： ウィキペディア英語版 correlation integral In chaos theory, the correlation integral is the mean probability that the states at two different times are close: :$C(\backslash varepsilon)\; =\; \backslash lim\_\; \backslash frac\; \backslash sum\_\}^N\; \backslash Theta(\backslash varepsilon\; -\; ||\; \backslash vec(i)\; -\; \backslash vec(j)||),\; \backslash quad\; \backslash vec(i)\; \backslash in\; \backslash Bbb^m,$ where $N$ is the number of considered states $\backslash vec(i)$, $\backslash varepsilon$ is a threshold distance, $||\; \backslash cdot\; ||$ a norm (e.g. Euclidean norm) and $\backslash Theta(\; \backslash cdot\; )$ the Heaviside step function. If only a time series is available, the phase space can be reconstructed by using a time delay embedding (see Takens' theorem): :$\backslash vec(i)\; =\; (u(i),\; u(i+\backslash tau),\; \backslash ldots,\; u(i+\backslash tau(m-1)),$ where $u(i)$ is the time series, $m$ the embedding dimension and $\backslash tau$ the time delay. The correlation integral is used to estimate the correlation dimension. An estimator of the correlation integral is the correlation sum: :$C(\backslash varepsilon)\; =\; \backslash frac\; \backslash sum\_\}^N\; \backslash Theta(\backslash varepsilon\; -\; ||\; \backslash vec(i)\; -\; \backslash vec(j)||),\; \backslash quad\; \backslash vec(i)\; \backslash in\; \backslash Bbb^m.$ ==See also== *Recurrence quantification analysis 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「correlation integral」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.