Sandro Rautenberg, F Luciano, de Aka Ana Karla Medeiros et al. · 2008
This paper presents some of the procedures adopted in the construction of a Radial Basis Function Neural Network by iteratively applying the aiNET, an Artificial Immune Systems Algorithm. These procedures have shown to be effective in terms of i) the free determination of centroids inspired by an immune heuristics; and ii) the achievement of appropriate minimal square errors after a number of iterations. Experimental and empirical results are compared aiming at confirming (or not) some hypotheses.
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Fabio Matera · Substance Use & Misuse · 1998
Cited by 27
Nevoral, Leoš · Brno University of Technology Digital Library (Brno University of Technology) · 2024
Práce se zabývá přiblížením problematiky RBF neuronových sítí a specificky RCE sítě pomocí demo aplikace. V demo aplikaci je hlavně vizualizovaný proces učení sítě, ale i stav neuronové sítě a různé tvary bázových funkcí. Dále je také zkoumáno využití EBF neuronových sítí. Klasické přístupy k EBF sítím jsou srovnány s novým návrhem OEBF sítě a následně jsou otestovány. Tento nový návrh je založený na vytváření eliptických oblastí pomocí euklidovské vzdálenosti od ohnisek elipsy. Nový návrh nejeví známky vylepšení vlastností těchto sítí a naopak spíše produkuje skoro stejné výsledky jako klasická RCE síť, které jsou ale řádově asi o jednotky procent méně přesné. Na závěr jsou navrženy možnosti pro budoucí úpravy tohoto přístupu.
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N. Delannay, F. Rossi, B. Conan-guez et al. · 2004
Abstract. There has been recently a lot of interest for functional data analysis [1] and extensions of well-known methods to functional inputs (clustering algorithm [2], non-parametric models [3], MLP [4]). The main motivation of these methods is to benefit from the enforced inner structure of the data. This paper presents how functional data can be used with RBFN, and how the inner structure of the former can help designing the network. 1
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M. Heiss, S. Kampl · IEEE Transactions on Neural Networks · 1996
For the purpose of adaptive function approximation, a new radial basis function network is proposed which is nonlinear in its parameters. The goal is to reduce significantly the computational effort for a serial processor, by avoiding multiplication in both the evaluation of the function model and the computation of the parameter adaptation. The approximation scheme makes use of a grid-based Gaussian basis function network. Due to the local support of digitally implemented Gaussian functions the function representation is parametric local and therefore well suited for an online implementation on a microcomputer. A gradient descent based nonlinear learning algorithm is presented and the convergence of the algorithm is proved.
Cited by 15
S. Kampl, M. Heiss · 2005
For the purpose of adaptive function approximation, a new approximation scheme is proposed which is nonlinear in its parameters. The goal is to reduce significantly the computational effort for a serial processor, by avoiding multiplication in both the evaluation of the function model and the computation of the parameter adaptation. The approximation scheme makes use of a grid-based Gaussian basis function network. Due to the local support of digitally implemented Gaussian functions, the function representation is parametric local and therefore well-suited for an implementation on a microcomputer. A gradient descent based nonlinear learning algorithm is presented and the convergence of the algorithm is proved.
Cited by 1
Rami N. Mahdi (373867), Eric C. Rouchka (157872) · Figshare · 2015
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Gancho Vachkov, Alok Sharma · 2014
In this paper a learning algorithm for creating a Growing Radial Basis Function Network (RBFN) Model is presented and analyzed. The main concept of this algorithm is that the number of the Radial Basis Function (RBF) units is gradually increased at each learning step of the algorithm and the model is gradually improved, until a predetermined (desired) approximation error is achieved. The important point here is that at each step of increasing the number of the RBF units, an optimization algorithm is run to optimize the parameters of only this unit, while keeping the parameters of all the previously optimized RBF units. Such strategy, even if being suboptimal, leads to significant reduction in the number of the parameters that have to be optimized at each step. A modified constraint version of the particle swarm optimization (PSO) algorithm with inertia weight is develop and used in this paper. It allows for obtaining optimal solutions with clear practical meaning. A synthetic nonlinear test example is used in the paper to analyze the performance of the proposed learning algorithm for creating the Growing RBFN model. A comparison with the standard algorithm for simultaneous optimization of all parameters of the classical RBFN model with fixed number of units is also done. It shows that the learning of the Growing RBFN model leads to a more stable and in many cases more accurate solution.
Cited by 3
Giulia Antinori · Bulletin of Miscellaneous Information (Royal Gardens Kew)
Study of a new method for the numerical solution of ODEs systems which arise from biological models. In particular, we consider a method which makes use of a Radial Basis Function Network (RBFN) and it is applied to a biological model for diabetes and insulin therapy.
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Adrian G. Borş, Ioannis Pitas · IEEE Transactions on Neural Networks · 1996
Radial 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 different statistical approaches. The first approach uses classical estimation in the learning stage and it is based on the learning vector quantization algorithm and its second-order statistics extension. After the presentation of this approach, we introduce the median radial basis function (MRBF) algorithm based on robust estimation of the hidden unit parameters. The proposed algorithm employs the marginal median for kernel location estimation and the median of the absolute deviations for the scale parameter estimation. A histogram-based fast implementation is provided for the MRBF algorithm. The theoretical performance of the two training algorithms is comparatively evaluated when estimating the network weights. The network is applied in pattern classification problems and in optical flow segmentation.
Cited by 162
Hu-ming Cheung · 2004
Cheung and Xu (2001) has presented a dual structural recurrent radial basis function (RBF) network by considering the different scales in net's inputs and outputs. However, such a network implies that the underlying functional relationship between the net's inputs and outputs is linear separable, which may not be true from a practical viewpoint. In this paper, we therefore propose a new recurrent RBF network. It takes the net's input and the past outputs as an augmented input in analogy with the one in Billings and Fung (1995), but introduces a scale tuner into the net's hidden layer to balance the different scales between inputs and outputs. This network adaptively learns the parameters in the hidden layer together with those in the output layer. We implement this network by using a variant of extended normalized RBF (Cheung and Xu (2001)) with its hidden units learned by the rival penalization controlled competitive learning algorithm. The experiments have shown the outstanding performance of the proposed network in recursive function estimation.
Cited by 6
Peng Zhang (2071), Keping Liu (795347), Bo Zhao (13553) et al. · Figshare · 2016
<p>This figure illustrates the model of the RBFNN. The network has three layers: the input layer, the middle layer and the output layer. The input of the network is passed to all neurons by the input layer. In the middle layer, the neurons of the radial basis function output values based on the inputs. The output of the network is the sum of the outputs of the neurons with different coefficients by the output layer.</p>
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Chi-Bin Cheng, E. Stanley Lee · Fuzzy Sets and Systems · 2001
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Ch. Venkateswarlu · Elsevier eBooks · 2025
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Zhong-qiu Zhao, De-shuang Huang, Lin Guo · 2015
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R. Preethi, G. Sathiyapriya, S. Shanthi · Materials Today Proceedings · 2022
Cited by 5
Andrew J. Waddie, Mohammad R. Taghizadeh · 2006
The radial basis function network (RBFN) is a multi-layer feed-forward neural network consisting of simple processing elements (neurons) with weighted interconnections between the elements. The weighted interconnections between the neurons can be calculated by any one of a wide range of optimisation algorithms. We will demonstrate that although the gradient descent method produces a "better" solution to the sample problem, limiting the number of allowable interconnection weights enhances the tolerance of the network to errors in the DOE reconstruction. In addition, the genetic algorithm optimisation method is significantly faster than the gradient descent method for the same number of allowable weight values.
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Yiu‐ming Cheung · 2003
Cheung and Xu 2001 has presented a dual structural recurrent radial basis function (RBF) network by considering the different scales in net’s inputs and outputs. However, such a network implies that the underlying functional relationship between the net’s inputs and outputs is linear separable, which may not be true from a practical viewpoint. In this paper, we therefore propose a new recurrent RBF network. It takes the net’s input and the past outputs as an augmented input in analogy with the one in (Billings and Fung 1995), but introduces a scale tuner into the net’s hidden layer to balance the different scales between inputs and outputs. This network adaptively learns the parameters in the hidden layer together with those in the output layer. We implement this network by using a variant of extended normalized RBF (Cheung and Xu 2001) with its hidden units learned by the rival penalization controlled competitive learning (RPCCL) algorithm (Cheung 2002). The experiments have shown the outstanding performance of the proposed network in recursive function estimation.
Cited by 2
S. Abisha (15188270), A. M Mutawa (15188273), Murugappan Murugappan (849001) et al. · Figshare · 2023
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F. Heimes, B. van Heuveln · 2002
Presents a neural network called the normalized radial basis function (NRBF) neural network. The NRBF integrates techniques from two similar neural networks: the general regression neural network (GRNN) and the radial basis function (RBF) neural network. The NRBF is identical to the standard radial basis function (RBF) network except the hidden layer outputs are normalized before being passed through the output layer. The normalization of the hidden layer weights is shown to improve the extrapolation performance of the conventional RBF network. We have reason to believe that under normal circumstances the NRBF outperforms the RBF and the GRNN.
Cited by 42