Relaxed conditions for radial-basis function networks to be universal approximators

Liao, Yi; Fang, Shu‐Cherng; Nuttle, Henry L. W.

doi:10.1016/s0893-6080(02)00227-7

Cited by 96 publications

(47 citation statements)

References 9 publications

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“…Although there have been theoretical proofs for the capability of FNNs [1]- [4], how to train FNNs is still a challenging problem and various objective functions have been proposed to improve the training of FNNs [5]- [11]. These functions have peculiar properties and they can be compared various ways.…”

Section: Introductionmentioning

confidence: 99%

Contour Plots of Objective Functions for Feed-Forward Neural Networks

Oh¹

2012

International Journal of Contents

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Section: Introductionmentioning

confidence: 99%

Contour Plots of Objective Functions for Feed-Forward Neural Networks

Oh¹

2012

International Journal of Contents

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“…The RBFNs are under continuously research, so we can find abundant literature about extensions and improvements of RBFNs learning and modeling (Billings, Wei, & Balikhin, 2007;Ghodsi & Schuurmans, 2003;Lázaro, Santamaría, & Pantaleón, 2003;Wallace, Tsapatsoulis, & Kollias, 2005;Wei & Amari, 2008). Recently, we can find some work analyzing the behavior of RBFNs (Eickhoff & Ruckert, 2007;Liao, Fang, & Nuttle, 2003;Yeung, Ng, Wang, Tsang, & Wang, 2007) and improving their efficiency (Arenas-Garcia, Gomez-Verdejo, & Figueiras-Vidal, 2007;Schwenker, Kestler, & Palm, 2001). As we can see from the recent and past literature, we can conclude that RBFNs are a widely employed and well-known model which is actually used.…”

Section: Radial Basis Function Network: Short Outlook and Descriptionmentioning

confidence: 99%

Radial Basis Function Networks

Silva

Spatti

Flauzino

et al. 2016

Artificial Neural Networks

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a b s t r a c tThe presence of Missing Values in a data set can affect the performance of a classifier constructed using that data set as a training sample. Several methods have been proposed to treat missing data and the one used more frequently is the imputation of the Missing Values of an instance.In this paper, we analyze the improvement of performance on Radial Basis Function Networks by means of the use of several imputation methods in the classification task with missing values. The study has been conducted using data sets with real Missing Values, and data sets with artificial Missing Values. The results obtained show that EventCovering offers a very good synergy with Radial Basis Function Networks. It allows us to overcome the negative impact of the presence of Missing Values to a certain degree.

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“…In complex multi-objective problems, the adoption of universal approximators is generally preferred as it provides more flexibility to the shape of the control policy. In this paper, we define the parameterized policy ⇡ ✓ using Artificial Neural Networks (e.g., Hornik et al, 1989) and gaussian Radial Basis Functions (e.g., Liao et al, 2003). The policy input vector t includes the system state x t , with the resulting policy characterized by a closed feedback loop.…”

Section: Universals Approximatorsmentioning

confidence: 99%

“…In practice, the optimal training of the approximator, and thus its accuracy, strongly depends on the parameters domain, on the dimensions of the input (state) and output (control) sets, and on the size of the training dataset available (Kurková and Sanguineti, 2001). In this paper, we comparatively analyze two among the most commons universal approximators: Artificial Neural Networks (Hornik et al, 1989) and Radial Basis Functions (Liao et al, 2003). In particular, we assess their e↵ectiveness under di↵erent sets of input to estimate their scalability to high-dimensional state space problems.…”

Section: Introductionmentioning

confidence: 99%

Universal approximators for direct policy search in multi-purpose water reservoir management: A comparative analysis

Giuliani

Mason

Castelletti

et al. 2014

IFAC Proceedings Volumes

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This study presents a novel approach which combines direct policy search and multi-objective evolutionary algorithms to solve high-dimensional state and control space water resources problems involving multiple, conflicting, and non-commensurable objectives. In such a multi-objective context, the use of universal function approximators is generally suggested to provide flexibility to the shape of the control policy. In this paper, we comparatively analyze Artificial Neural Networks (ANN) and Radial Basis Functions (RBF) under di↵erent sets of input to estimate their scalability to high-dimensional state space problems. The multi-purpose HoaBinh water reservoir in Vietnam, accounting for hydropower production and flood control, is used as a case study. Results show that the RBF policy parametrization is more e↵ective than the ANN one. In particular, the approximated Pareto front obtained with RBF control policies successfully explores the full tradeo↵ space between the two conflicting objectives, while the ANN solutions are often Pareto-dominated by the RBF ones.

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Relaxed conditions for radial-basis function networks to be universal approximators

Cited by 96 publications

References 9 publications

Contour Plots of Objective Functions for Feed-Forward Neural Networks

Contour Plots of Objective Functions for Feed-Forward Neural Networks

Radial Basis Function Networks

Universal approximators for direct policy search in multi-purpose water reservoir management: A comparative analysis

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