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Hermite Radial Basis Functions Implicits
Computer Graphics Forum, 2010Abstract 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 Macêdo +2 more
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A practical radial basis function equalizer
IEEE Transactions on Neural Networks, 1999A 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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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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Optimising the widths of radial basis functions
Proceedings 5th Brazilian Symposium on Neural Networks (Cat. No.98EX209), 2002In the context of regression analysis with penalised linear models (such as RBF networks) certain model selection criteria can be differentiated to yield a re-estimation formula for the regularisation parameter such that an initial guess can be iteratively improved until a local minimum of the criterion is reached.
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Animated deformations with radial basis functions
Proceedings of the ACM symposium on Virtual reality software and technology - VRST '00, 2000We present a novel approach to creating deformations of polygonal models using Radial Basis Functions (RBFs) to produce localized real-time deformations. Radial Basis Functions assume surface smoothness as a minimal constraint and animations produce smooth displacements of affected vertices in a model.
Jun-yong Noh +2 more
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Solving PDEs with radial basis functions
Acta Numerica, 2015Finite differences provided the first numerical approach that permitted large-scale simulations in many applications areas, such as geophysical fluid dynamics. As accuracy and integration time requirements gradually increased, the focus shifted from finite differences to a variety of different spectral methods.
Bengt Fornberg, Natasha Flyer
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Gradient Descent and Radial Basis Functions
2006In this paper, we present experiments comparing different training algorithms for Radial Basis Functions (RBF) neural networks. In particular we compare the classical training which consists of an unsupervised training of centers followed by a supervised training of the weights at the output, with the full supervised training by gradient descent ...
Mercedes Fernández-Redondo +2 more
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RBFA: Radial Basis Function Autoencoders
2019 IEEE Congress on Evolutionary Computation (CEC), 2019We 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, 1993This 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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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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