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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 Approximate entropy ： ウィキペディア英語版 Approximate entropy In statistics, an approximate entropy (ApEn) is a technique used to quantify the amount of regularity and the unpredictability of fluctuations over time-series data.〔 〕 For example, there are two series of data: : series 1: (10,20,10,20,10,20,10,20,10,20,10,20...), which alternates 10 and 20. : series 2: (10,10,20,10,20,20,20,10,10,20,10,20,20...), which has either a value of 10 or 20, chosen randomly, each with probability 1/2. Moment statistics, such as mean and variance, will not distinguish between these two series. Nor will rank order statistics distinguish between these series. Yet series 1 is "perfectly regular"; knowing one term has the value of 20 enables one to predict with certainty that the next term will have the value of 10. Series 2 is randomly valued; knowing one term has the value of 20 gives no insight into what value the next term will have. Regularity was originally measured by exact regularity statistics, which has mainly centered on various entropy measures.〔 However, accurate entropy calculation requires vast amounts of data, and the results will be greatly influenced by system noise,〔 〕 therefore it is not practical to apply these methods to experimental data. ApEn was developed by Steve M. Pincus to handle these limitations by modifying an exact regularity statistic, Kolmogorov–Sinai entropy. ApEn was initially developed to analyze medical data, such as heart rate,〔 and later spread its applications in finance,〔 〕 psychology,〔 〕 and human factors engineering.〔 〕 ==The algorithm== $\backslash text$: Form a time series of data $\backslash \; u(1),\; u(2),\backslash ldots,\; u(N)$. These are $\backslash text$ raw data values from measurement equally spaced in time. $\backslash text$: Fix $\backslash \; m$, an integer, and $\backslash \; r$, a positive real number. The value of $\backslash \; m$ represents the length of compared run of data, and $\backslash \; r$ specifies a filtering level. $\backslash text$: Form a sequence of vectors $\backslash mathbf(1)$,$\backslash mathbf(2),\backslash ldots,\backslash mathbf(N-m+1)$, in $\backslash mathbf^$, real $\backslash \; m$-dimensional space defined by $\backslash mathbf(i)\; =\; ()$. $\backslash text$: Use the sequence $\backslash mathbf(1)$,$\backslash mathbf(2),\backslash ldots,\backslash mathbf(N-m+1)$ to construct, for each $\backslash \; i$, $1\; \backslash le\; i\; \backslash le\; N-m+1$ : in which $\backslash \; d(x^$ * ) is defined as : *(a)| \, The $\backslash \; u(a)$ are the $\backslash text$ scalar components of $\backslash mathbf$. $\backslash \; d$ represents the distance between the vectors $\backslash mathbf(i)$ and $\backslash mathbf(j)$, given by the maximum difference in their respective scalar components. Note that $j$ takes on all values, so the match provided when $i=j$ will be counted (the subsequence is matched against itself). $\backslash text$: Define :$\backslash Phi\; ^m\; (r)\; =\; (N-m+1)^\; \backslash sum\_^log(C\_i^m\; (r))$, $\backslash text$: Define approximate entropy $\backslash \; (\backslash mathrm)$ as :$\backslash \; \backslash mathrm\; =\; \backslash Phi\; ^m\; (r)\; -\; \backslash Phi^\; (r).$ where $\backslash \; log$ is the natural logarithm, for $\backslash \; m$ and $\backslash \; r$ fixed as in Step 2. Parameter selection: typically choose $\backslash \; m=2$ or $\backslash \; m=3$, and $\backslash \; r$ depends greatly on the application. An implementation on Physionet,〔()〕 which is based on Pincus 〔 use whereas the original article uses $d()\; \backslash le\; r$ in Step 4. While a concern for artificially constructed examples, it is usually not a concern in practice. 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「Approximate entropy」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.