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Radial Basis Function Networks
2013Learning is an approximation problem, which is closely related to the conventional approximation techniques, such as generalized splines and regularization techniques. The RBF network has its origin in performing exact interpolation of a set of data points in a multidimensional space [81].
Ke-Lin Du, M. N. S. Swamy
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Adaptive radial basis functions
Proceedings of 13th International Conference on Pattern Recognition, 1996We develop adaptive radial basis functions: kernel-based models for regression and discrimination where the functional form of the basis function depends on the data. The approach may be regarded as a radial form of projection pursuit, with the additional constraint that the basis functions have a common functional form.
A.R. Webb, S. Shannon
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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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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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