Optimising the widths of radial basis functions

Orr, Mark J. L.

doi:10.1109/sbrn.1998.730989

Cited by 37 publications

(31 citation statements)

References 4 publications

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“…Their experimental outcomes have shown that the nonsymmetric partition can lead to the development of more accurate RBF models, with a smaller number of hidden layer nodes. More elaborate methods have been suggested [58][59][60][61] for optimizing the RBF widths in order to improve approximation accuracy. Taking advantage of the linear connection between the hidden and output layer, most training algorithms calculate the synaptic weights of RBF networks by applying linear regression of the output of the hidden units on the target values.…”

Section: Orthogonal Least Squares (Ols)mentioning

confidence: 99%

Where are Universals?

Peacock¹

2016

Metaphysica

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Radial basis function networks (RBFNs) have gained widespread appeal amongst researchers and have shown good performance in a variety of application domains. They have potential for hybridization and demonstrate some interesting emergent behaviors. This paper aims to o er a compendious and sensible survey on RBF networks. The advantages they o er, such as fast training and global approximation capability with local responses, are attracting many researchers to use them in diversi ed elds. The overall algorithmic development of RBF networks by giving special focus on their learning methods, novel kernels, and ne tuning of kernel parameters have been discussed. In addition, we have considered the recent research work on optimization of multi-criterions in RBF networks and a range of indicative application areas along with some open source RBFN tools.

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Section: Orthogonal Least Squares (Ols)mentioning

confidence: 99%

Where are Universals?

Peacock¹

2016

Metaphysica

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“…Basically, there are two categories of learning algorithms proposed for RBFNNs. The first category of learning algorithms simply places one RBF at each sample [10]. If all the training samples are selected as hidden centers, the generalization capability of the network will become so poor that many noised or deformed samples will not be recognized.…”

Section: Related Workmentioning

confidence: 99%

Logistic Regression by Means of Evolutionary Radial Basis Function Neural Networks

Gutiérrez

Hervás-Martı́nez

Martínez-Estudillo

2011

IEEE Trans. Neural Netw.

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Abstract-This paper proposes a hybrid multilogistic methodology, named logistic regression using initial and radial basis function (RBF) covariates. The process for obtaining the coefficients is carried out in three steps. First, an evolutionary programming (EP) algorithm is applied, in order to produce an RBF neural network (RBFNN) with a reduced number of RBF transformations and the simplest structure possible. Then, the initial attribute space (or, as commonly known as in logistic regression literature, the covariate space) is transformed by adding the nonlinear transformations of the input variables given by the RBFs of the best individual in the final generation. Finally, a maximum likelihood optimization method determines the coefficients associated with a multilogistic regression model built in this augmented covariate space. In this final step, two different multilogistic regression algorithms are applied: one considers all initial and RBF covariates (multilogistic initial-RBF regression) and the other one incrementally constructs the model and applies cross validation, resulting in an automatic covariate selection [simplelogistic initial-RBF regression (SLIRBF)]. Both methods include a regularization parameter, which has been also optimized. The methodology proposed is tested using 18 benchmark classification problems from well-known machine learning problems and two real agronomical problems. The results are compared with the corresponding multilogistic regression methods applied to the initial covariate space, to the RBFNNs obtained by the EP algorithm, and to other probabilistic classifiers, including different RBFNN design methods [e.g., relaxed variable kernel density estimation, support vector machines, a sparse classifier (sparse multinomial logistic regression)] and a procedure similar to SLIRBF but using product unit basis functions. The SLIRBF models are found to be competitive when compared with the corresponding multilogistic regression methods and the RBFEP method. A measure of statistical significance is used, which indicates that SLIRBF reaches the state of the art.

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“…This domain has been widely used in RBNN literature [5,8,17]. A random sampling with an uniform distribution over the interval ½ 4; 4 is used in order to obtain 40 input output points for the training data.…”

Section: Domains Descriptionmentioning

confidence: 99%

Learning radial basis neural networks in a lazy way: A comparative study

2008

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a b s t r a c tLazy learning methods have been used to deal with problems in which the learning examples are not evenly distributed in the input space. They are based on the selection of a subset of training patterns when a new query is received. Usually, that selection is based on the k closest neighbors and it is a static selection, because the number of patterns selected does not depend on the input space region in which the new query is placed. In this paper, a lazy strategy is applied to train radial basis neural networks. That strategy incorporates a dynamic selection of patterns, and that selection is based on two different kernel functions, the Gaussian and the inverse function. This lazy learning method is compared with the classical lazy machine learning methods and with eagerly trained radial basis neural networks.

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Optimising the widths of radial basis functions

Cited by 37 publications

References 4 publications

Where are Universals?

Where are Universals?

Logistic Regression by Means of Evolutionary Radial Basis Function Neural Networks

Learning radial basis neural networks in a lazy way: A comparative study

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