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Radial Basis Functions

2014
This last chapter may be seen as a general introduction to meshless methods, not only for surface reconstruction but in other problems of scattered data. The general interpolation and smoothing problems are described in terms of radial basis functions; we then illustrate some characterizations of these functions.
Hebert Montegranario, Jairo Espinosa
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A practical radial basis function equalizer

IEEE Transactions on Neural Networks, 1999
A radial basis function (RBF) equalizer design process has been developed in which the number of basis function centers used is substantially fewer than conventionally required. The reduction of centers is accomplished in two-steps. First an algorithm is used to select a reduced set of centers that lie close to the decision boundary.
Jungsik Lee   +2 more
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Radial Basis Functions

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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Shape-adaptive radial basis functions

IEEE Transactions on Neural Networks, 1998
Radial basis functions for discrimination and regression have been used with some success in a wide variety of applications. Here, we investigate the optimal choice for the form of the basis functions and present an iterative strategy for obtaining the function in a regression context using a conjugate gradient-based algorithm together with a ...
Andrew R. Webb, Simon Shannon
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Visualization of radial basis function networks

IJCNN'99. International Joint Conference on Neural Networks. Proceedings (Cat. No.99CH36339), 2003
Presents a method for the 3D visualization of the structure of radial basis function networks. This method allows the visualization of basis function characteristics (centers and widths) along with second level weights. Network properties can be displayed simultaneously with the training data or test data in the same input space.
Adrian K. Agogino   +2 more
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Hermite Radial Basis Functions Implicits

Computer Graphics Forum, 2010
Abstract The Hermite radial basis functions (HRBF) implicits reconstruct an implicit function which interpolates or approximates scattered multivariate Hermite data (i.e. unstructured points and their corresponding normals). Experiments suggest that HRBF implicits allow the reconstruction of surfaces rich in details and behave better than previous ...
Ives MacĂȘdo   +2 more
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RBFA: Radial Basis Function Autoencoders

2019 IEEE Congress on Evolutionary Computation (CEC), 2019
We are introducing a new variation of the existing autoencoder called Radial Basis Function Autoencoders (RBFA). This version employs radial symmetric functions, in the first step of encoding, to map the input data vectors into a new form. The transformation which relies on the similarity between the input data examples and predefined center points ...
Maisa Daoud   +2 more
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Approximation and Radial-Basis-Function Networks

Neural Computation, 1993
This paper concerns conditions for the approximation of functions in certain general spaces using radial-basis-function networks. It has been shown in recent papers that certain classes of radial-basis-function networks are broad enough for universal approximation. In this paper these results are considerably extended and sharpened.
Jooyoung Park, Irwin W. Sandberg
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Radial Basis Functions

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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Radial Basis Functions

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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