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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 Radial basis function ： ウィキペディア英語版 Radial basis function A radial basis function (RBF) is a real-valued function whose value depends only on the distance from the origin, so that $\backslash phi(\backslash mathbf)\; =\; \backslash phi(\backslash |\backslash mathbf\backslash |)$; or alternatively on the distance from some other point ''c'', called a ''center'', so that $\backslash phi(\backslash mathbf,\; \backslash mathbf)\; =\; \backslash phi(\backslash |\backslash mathbf-\backslash mathbf\backslash |)$. Any function $\backslash phi$ that satisfies the property $\backslash phi(\backslash mathbf)\; =\; \backslash phi(\backslash |\backslash mathbf\backslash |)$ is a radial function. The norm is usually Euclidean distance, although other distance functions are also possible. Sums of radial basis functions are typically used to approximate given functions. This approximation process can also be interpreted as a simple kind of neural network; this was the context in which they originally surfaced, in work by David Broomhead and David Lowe in 1988,〔(Radial Basis Function networks )〕 which stemmed from Michael J. D. Powell's seminal research from 1977.〔: "We would like to thank Professor M.J.D. Powell at the Department of Applied Mathematics and Theoretical Physics at Cambridge University for providing the initial stimulus for this work."〕 RBFs are also used as a kernel in support vector classification. == Types == Commonly used types of radial basis functions include (writing $r\; =\; \backslash |\backslash mathbf\; -\; \backslash mathbf\_i\backslash |\backslash ;$): * Gaussian: The first term, that is used for normalisation of the Gaussian, is missing, because in our sum every Gaussian has a weight, so the normalisation is not necessary. ::$\backslash phi(r)\; =\; e^\backslash ,$ * Multiquadric: ::$\backslash phi(r)\; =\; \backslash sqrt$ * Inverse quadratic: ::$\backslash phi(r)\; =\; \backslash frac$ * Inverse multiquadric: ::$\backslash phi(r)\; =\; \backslash frac\{\backslash sqrt\{1\; +\; (\backslash varepsilon\; r)^2\}\}$ * Polyharmonic spline: ::$\backslash phi(r)\; =\; r^k,\backslash ;\; k=1,3,5,\backslash dots$ ::$\backslash phi(r)\; =\; r^k\; \backslash ln(r),\backslash ;\; k=2,4,6,\backslash dots$ * Thin plate spline (a special polyharmonic spline): ::$\backslash phi(r)\; =\; r^2\; \backslash ln(r)\backslash ;$ 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「Radial basis function」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.