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Robustness of radial basis functions
Neurocomputing, 2005Neural networks are intended to be used in future nanoelectronic technology since these architectures seem to be robust to malfunctioning elements and noise in its inputs and parameters. In this work, the robustness of radial basis function networks is analyzed in order to operate in noisy and unreliable environment.
Eickhoff, Ralf, Rückert, Ulrich
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Kolmogorov-Arnold Networks are Radial Basis Function Networks
arXiv.orgThis short paper is a fast proof-of-concept that the 3-order B-splines used in Kolmogorov-Arnold Networks (KANs) can be well approximated by Gaussian radial basis functions.
Ziyao Li
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2019
Many sciences and other areas of research and applications from engineering to economics require the approximation of functions that depend on many variables. This can be for a variety of reasons. Sometimes we have a discrete set of data points and we want to find an approximating function that completes this data; another possibility is that precise ...
Buhmann, Martin, Jäger, Janin
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Many sciences and other areas of research and applications from engineering to economics require the approximation of functions that depend on many variables. This can be for a variety of reasons. Sometimes we have a discrete set of data points and we want to find an approximating function that completes this data; another possibility is that precise ...
Buhmann, Martin, Jäger, Janin
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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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