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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 Variable kernel density estimation ： ウィキペディア英語版 Variable kernel density estimation In statistics, adaptive or "variable-bandwidth" kernel density estimation is a form of kernel density estimation in which the size of the kernels used in the estimate are varied depending upon either the location of the samples or the location of the test point. It is a particularly effective technique when the sample space is multi-dimensional. 〔 〕 ==Rationale== Given a set of samples, $\backslash lbrace\; \backslash vec\; x\_i\; \backslash rbrace$, we wish to estimate the density, $P(\backslash vec\; x)$, at a test point, $\backslash vec\; x$: : $$ P(\vec x) \approx \frac : $$ W = \sum_^n w_i : $$ w_i = K \left ( \frac \right ) where ''n'' is the number of samples, ''K'' is the "kernel", ''h'' is its width and ''D'' is the number of dimensions in $\backslash vec\; x$. The kernel can be thought of as a simple, linear filter. Using a fixed filter width may mean that in regions of low density, all samples will fall in the tails of the filter with very low weighting, while regions of high density will find an excessive number of samples in the central region with weighting close to unity. To fix this problem, we vary the width of the kernel in different regions of the sample space. There are two methods of doing this: balloon and pointwise estimation. In a balloon estimator, the kernel width is varied depending on the location of the test point. In a pointwise estimator, the kernel width is varied depending on the location of the sample.〔 For multivariate estimators, the parameter, ''h'', can be generalized to vary not just the size, but also the shape of the kernel. This more complicated approach will not be covered here. 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「Variable kernel density estimation」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.