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Comparison of Radial Basis Functions
Numerical Analysis and Applications, 2018Summary: A survey of algorithms for approximation of multivariate functions with radial basis function (RBF) splines is presented. Algorithms of interpolating, smoothing, selecting the smoothing parameter, and regression with splines are described in detail.
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1995
Abstract The network models discussed in Chapters 3 and 4 are based on units which compute a non-linear function of the scalar product of the input vector and a weight vector. Here we consider the other major class of neural network model, in which the activation of a hidden unit is determined by the distance between the input vector and
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Abstract The network models discussed in Chapters 3 and 4 are based on units which compute a non-linear function of the scalar product of the input vector and a weight vector. Here we consider the other major class of neural network model, in which the activation of a hidden unit is determined by the distance between the input vector and
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2017
In this chapter the RBF mathematical concepts are exposed considering firstly the interpolation problem with the RBF function defined by known values at source points; a first hands-on example is provided showing how RBF work. Further topics of RBF theory are then introduced considering the differentiation of RBF, the fitting of an RBF with known ...
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In this chapter the RBF mathematical concepts are exposed considering firstly the interpolation problem with the RBF function defined by known values at source points; a first hands-on example is provided showing how RBF work. Further topics of RBF theory are then introduced considering the differentiation of RBF, the fitting of an RBF with known ...
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2001
This chapter considers radial basis function (RBF) networks. A RBF network can be described as a parametrized model used to approximate an arbitrary function by means of a linear combination of basic functions. RBF networks belong to the class of kernel function networks where the inputs to the model are passed through kernel functions which limit the ...
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This chapter considers radial basis function (RBF) networks. A RBF network can be described as a parametrized model used to approximate an arbitrary function by means of a linear combination of basic functions. RBF networks belong to the class of kernel function networks where the inputs to the model are passed through kernel functions which limit the ...
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2003
In many areas of mathematics, science and engineering, from computer graphics to inverse methods to signal processing, it is necessary to estimate parameters, usually multidimensional, by approximation and interpolation. Radial basis functions are a powerful tool which work well in very general circumstances and so are becoming of widespread use as the
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In many areas of mathematics, science and engineering, from computer graphics to inverse methods to signal processing, it is necessary to estimate parameters, usually multidimensional, by approximation and interpolation. Radial basis functions are a powerful tool which work well in very general circumstances and so are becoming of widespread use as the
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Applying radial basis functions
IEEE Signal Processing Magazine, 1996Discusses the application of neural networks to general and radial basis functions and in particular to adaptive equalization and interference rejection problems. Neural-network-based algorithms strike a good balance between performance and complexity in adaptive equalization, and show promise in spread spectrum systems.
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2004
Radial basis functions are traditionaland powerful tools for multivariate scattered data interpolation.Much of the material presented in this chapter is essentially needed in the subsequent developments of this work,such as for the multi level approximation schemes in Chapter 5, and the mesh free simulation of transport processes in Chapter 6.
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Radial basis functions are traditionaland powerful tools for multivariate scattered data interpolation.Much of the material presented in this chapter is essentially needed in the subsequent developments of this work,such as for the multi level approximation schemes in Chapter 5, and the mesh free simulation of transport processes in Chapter 6.
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Spherical Radial Basis Functions
1998Abstract In this chapter we deal with spherical radial basis functions, i.e. kernel functions depending only on the (spherical) distance between unit vectors. The importance of our considerations lies in the development of general Sobolev spaces ℋ and (invariant) pseudodifferential operators Λ in which it is possible that (i) the radial ...
W Freeden, T Gervens, M Schreiner
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Median radial basis function neural network
IEEE Transactions on Neural Networks, 1996Radial basis functions (RBFs) consist of a two-layer neural network, where each hidden unit implements a kernel function. Each kernel is associated with an activation region from the input space and its output is fed to an output unit. In order to find the parameters of a neural network which embeds this structure we take into consideration two ...
A G, Bors, I, Pitas
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2007
This paper introduces new kernel radial basis functions (RBFs) which characterize partial differential equation problems of interest. Then we developed the meshfree collocation methods based on these kernel RBFs to solve benchmark Helmholtz, modified Helmholtz, and convection-diffusion problems.
W. Chen, H. Wang, Q. H. Qin
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This paper introduces new kernel radial basis functions (RBFs) which characterize partial differential equation problems of interest. Then we developed the meshfree collocation methods based on these kernel RBFs to solve benchmark Helmholtz, modified Helmholtz, and convection-diffusion problems.
W. Chen, H. Wang, Q. H. Qin
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