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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 Hyper basis function network ： ウィキペディア英語版 Hyper basis function network In machine learning, a Hyper basis function network, or HyperBF network, is a generalization of radial basis function (RBF) networks concept, where the Mahalanobis-like distance is used instead of Euclidean distance measure. Hyper basis function networks were first introduced by Poggio and Girosi in the 1990 paper “Networks for Approximation and Learning”.〔T. Poggio and F. Girosi (1990). "Networks for Approximation and Learning". ''Proc. of the IEEE'' Vol. 78, No. 9:1481-1497.〕〔R.N. Mahdi, E.C. Rouchka (2011). ("Reduced HyperBF Networks: Regularization by Explicit Complexity Reduction and Scaled Rprop-Based Training" ). ''IEEE Transactions of Neural Networks'' 2:673–686.〕 ==Network Architecture== The typical HyperBF network structure consists of a real input vector $x\backslash in\; \backslash mathbb^n$, a hidden layer of activation functions and a linear output layer. The output of the network is a scalar function of the input vector, $\backslash phi:\; \backslash mathbb^n\backslash to\backslash mathbb$, is given by $\backslash phi(x)=\backslash sum\_^a\_j\backslash rho\_j(||x-\backslash mu\_j||)$ where $N$ is a number of neurons in the hidden layer, $\backslash mu\_j$ and $a\_j$ are the center and weight of neuron $j$. The activation function $\backslash rho\_j(||x-\backslash mu\_j||)$ at the HyperBF network takes the following form $\backslash rho\_j(||x-\backslash mu\_j||)=e^$ where $R\_j$ is a positive definite $d\backslash times\; d$ matrix. Depending on the application, the following types of matrices $R\_j$ are usually considered〔F. Schwenker, H.A. Kestler and G. Palm (2001). "Three Learning Phases for Radial-Basis-Function Network" ''Neural Netw.'' 14:439-458.〕 * $R\_j=\backslash frac\backslash mathbb\_$, where $\backslash sigma>0$. This case corresponds to the regular RBF network. * $R\_j=\backslash frac\backslash mathbb\_$, where $\backslash sigma\_j>0$. In this case, the basis functions are radially symmetric, but are scaled with different width. * $R\_j=diag\backslash left(\backslash frac,...,\backslash frac\backslash right)\backslash mathbb\_$, where $\backslash sigma\_>0$. Every neuron has an elliptic shape with a varying size. * Positive definite matrix, but not diagonal. 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「Hyper basis function network」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.