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A. Saha, ChuanLin Wu, DunSung Tang, "Approximation, Dimension Reduction, and Nonconvex Optimization Using Linear Superpositions of Gaussians," IEEE Transactions on Computers, vol. 42, no. 10, pp. 12221233, October, 1993.  
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@article{ 10.1109/12.257708, author = {A. Saha and ChuanLin Wu and DunSung Tang}, title = {Approximation, Dimension Reduction, and Nonconvex Optimization Using Linear Superpositions of Gaussians}, journal ={IEEE Transactions on Computers}, volume = {42}, number = {10}, issn = {00189340}, year = {1993}, pages = {12221233}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.257708}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Approximation, Dimension Reduction, and Nonconvex Optimization Using Linear Superpositions of Gaussians IS  10 SN  00189340 SP1222 EP1233 EPD  12221233 A1  A. Saha, A1  ChuanLin Wu, A1  DunSung Tang, PY  1993 KW  linear superpositions of Gaussians; dimension reduction; nonconvex optimization; neural network approaches; function approximation; radial basis function; function approximation; neural nets; optimisation; polynomials. VL  42 JA  IEEE Transactions on Computers ER   
This paper concerns neural network approaches to function approximation and optimization using linear superposition of Gaussians (or what are popularly known as radial basis function (RBF) networks). The problem of function approximation is one of estimating an underlying function f, given samples of the form ((y/sub i/, x/sub i/); i=1,2,...,n; with y/sub i/=f(x/sub i/)). When the dimension of the input is high and the number of samples small, estimation of the function becomes difficult due to the sparsity of samples in local regions. The authors find that this problem of high dimensionality can be overcome to some extent by using linear transformations of the input in the Gaussian kernels. Such transformations induce intrinsic dimension reduction, and can be exploited for identifying key factors of the input and for the phase space reconstruction of dynamical systems, without explicitly computing the dimension and delay. They present a generalization that uses multiple linear projections onto scalars and successive RBF networks (MLPRBF) that estimate the function based on these scaler values. They derive some key properties of RBF networks that provide suitable grounds for implementing efficient search strategies for nonconvex optimization within the same framework.
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