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Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximation
 IEEE Transactions on Neural Networks
"... Abstract—This paper presents a multiobjective evolutionary algorithm to optimize radial basis function neural networks (RBFNNs) in order to approach target functions from a set of inputoutput pairs. The procedure allows the application of heuristics to improve the solution of the problem at hand by ..."
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Cited by 27 (7 self)
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Abstract—This paper presents a multiobjective evolutionary algorithm to optimize radial basis function neural networks (RBFNNs) in order to approach target functions from a set of inputoutput pairs. The procedure allows the application of heuristics to improve the solution of the problem at hand by including some new genetic operators in the evolutionary process. These new operators are based on two wellknown matrix transformations: singular value decomposition (SVD) and orthogonal least squares (OLS), which have been used to define new mutation operators that produce local or global modifications in the radial basis functions (RBFs) of the networks (the individuals in the population in the evolutionary procedure). After analyzing the efficiency of the different operators, we have shown that the global mutation operators yield an improved procedure to adjust the parameters of the RBFNNs. Index Terms—Evolutionary computation, neural networks, radial basis functions (RBFs), orthogonal transformations, heuristics.
Identification and Control of Dynamical Systems Using the SelfOrganizing Map
, 2004
"... In this paper, we introduce a general modeling technique, called VectorQuantized Temporal Associative Memory (VQTAM), which uses Kohonen's SelfOrganizing Map (SOM) as an alternative to MLP and RBF neural models for dynamical system identification and control. We demonstrate that the estimatio ..."
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Cited by 14 (6 self)
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In this paper, we introduce a general modeling technique, called VectorQuantized Temporal Associative Memory (VQTAM), which uses Kohonen's SelfOrganizing Map (SOM) as an alternative to MLP and RBF neural models for dynamical system identification and control. We demonstrate that the estimation errors decrease as the SOM training proceeds, allowing the VQTAM scheme to be understood as a selfsupervised gradientbased error reduction method. The performance of the proposed approach is evaluated on a variety of complex tasks, namely: (i) time series prediction, (ii) identification of SISO/MIMO systems, and (iii) nonlinear predictive control. For all tasks, the simulation results produced by the SOM are as accurate as those produced by the MLP network, and better than those produced by the RBF network. The SOM has also shown to be less sensitive to weight initialization than MLP networks. We conclude the paper by discussing the main properties of the VQTAM and their relationships to other wellestablished methods for dynamical system identification. We also suggest directions for further work.
Parallel Multiobjective Memetic RBFNNs Design and Feature Selection for Function Approximation Problems
"... Abstract. The design of Radial Basis Function Neural Networks (RBFNNs) still remains as a difficult task when they are applied to classification or to regression problems. The difficulty arises when the parameters that define an RBFNN have to be set, these are: the number of RBFs, the position of th ..."
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Cited by 10 (5 self)
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Abstract. The design of Radial Basis Function Neural Networks (RBFNNs) still remains as a difficult task when they are applied to classification or to regression problems. The difficulty arises when the parameters that define an RBFNN have to be set, these are: the number of RBFs, the position of their centers and the length of their radii. Another issue that has to be faced when applying these models to real world applications is to select the variables that the RBFNN will use as inputs. The literature presents several methodologies to perform these two tasks separately, however, due to the intrinsic parallelism of the genetic algorithms, a parallel implementation will allow the algorithm proposed in this paper to evolve solutions for both problems at the same time. The parallelization of the algorithm not only consists in the evolution of the two problems but in the specialization of the crossover and mutation operators in order to evolve the different elements to be optimized when designing RBFNNs. The subjacent Genetic Algorithm is the NonSorting Dominated Genetic Algorithm II (NSGAII) that helps to keep a balance between the size of the network and its approximation accuracy in order to avoid overtraining networks. Another of the novelties of the proposed algorithm is the incorporation of local search algorithms in three stages of the algorithm: initialization of the population, evolution of the individuals, and final optimization of the Pareto front. The initialization of the individuals is performed hybridizing clustering techniques with the Mutual Information theory (MI) to select the input variables. As the experiment will show, the synergy of the different paradigms and techniques combined by the presented algorithm allow to obtain very accurate models using the most significant input variables.
Improving the Performance of Multiobjective Genetic Algorithm for Function Approximation Through Parallel Islands Specialisation
 Lecture Notes in Artificial Intelligence
"... Abstract. Nature shows many examples where the specialisation of elements aimed to solve different problems is successful. There are explorer ants, worker bees, etc., where a group of individuals is assigned a specific task. This paper will extrapolate this philosophy, applying it to a multiobject ..."
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Cited by 6 (3 self)
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Abstract. Nature shows many examples where the specialisation of elements aimed to solve different problems is successful. There are explorer ants, worker bees, etc., where a group of individuals is assigned a specific task. This paper will extrapolate this philosophy, applying it to a multiobjective genetic algorithm. The problem to be solved is the design of Radial Basis Function Neural Networks (RBFNNs) that approximate a function. A non distributed multiobjective algorithm will be compared against a parallel approach that emerges as a straight forward specialisation of the crossover and mutation operators in different islands. The experiments will show how, as in the real world, if the different islands evolve specific aspects of the RBFNNs, the results are improved. 1
Studying possibility in a clustering algorithm for rbfnn design for function approximation
 Neural Computing and Applications
, 2008
"... The function approximation problem has been tackled many times in the literature by using Radial Basis Function Neural Networks (RBFNNs). In the design of these neural networks there are several stages where, the most critical stage is the initialization of the centers of each RBF since the rest of ..."
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Cited by 3 (1 self)
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The function approximation problem has been tackled many times in the literature by using Radial Basis Function Neural Networks (RBFNNs). In the design of these neural networks there are several stages where, the most critical stage is the initialization of the centers of each RBF since the rest of the steps to design the RBFNN strongly depend on it. The Improved Clustering for Function Approximation (ICFA) algorithm was recently introduced and proved successful for the function approximation problem. In the ICFA algorithm a fuzzy partition of the input data is performed but, a fuzzy partition can behave inadequately in noise conditions. Possibilistic and mixed approaches, combining fuzzy and possibilistic partitions, were developed in order to improve the performance of a fuzzy partition. In this paper, a study of the influence of replacing the fuzzy partition used in the ICFA algorithm with the possibilistic and the fuzzypossibilistic partitions will be done. A comparative analysis of each kind of partition will be performed in order to see if the possibilistic approach can improve the performance of the ICFA algorithm both in normal and in noise conditions. The results will show how the employment of a mixed approach combining fuzzy and possibilistic approach can lead to improve the results when designing RBFNNs. 1
A FuzzyPossibilistic Fuzzy Ruled Clustering Algorithm for RBFNNs Design
 Human IT. Borås Högskola
, 2000
"... Abstract. This paper presents a new approach to the problem of designing Radial Basis Function Neural Networks (RBFNNs) to approximate a given function. The presented algorithm focuses in the first stage of the design where the centers of the RBFs have to be placed. This task has been commonly solve ..."
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Abstract. This paper presents a new approach to the problem of designing Radial Basis Function Neural Networks (RBFNNs) to approximate a given function. The presented algorithm focuses in the first stage of the design where the centers of the RBFs have to be placed. This task has been commonly solved by applying generic clustering algorithms although in other cases, some specific clustering algorithms were considered. These specific algorithms improved the performance by adding some elements that allow them to use the information provided by the output of the function to be approximated but they did not add problem specific knowledge. The novelty of the new developed algorithm is the combination of a fuzzypossibilistic approach with a supervising parameter and the addition of a new migration step that, through the generation of RBFNNs, is able to take proper decisions on where to move the centers. The algorithm also introduces a fuzzy logic element by setting a fuzzy rule that determines the input vectors that influence each center position, this fuzzy rule considers the output of the function to be approximated and the fuzzypossibilistic partition of the data. 1
Multiobjective RBFNNs Designer for Function Approximation: An Application for Mineral Reduction
 Lecture Notes in Computer Science
"... Abstract. Radial Basis Function Neural Networks (RBFNNs) are well known because, among other applications, they present a good performance when approximating functions. The function approximation problem arises in the construction of a control system to optimize the process of the mineral reductio ..."
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Cited by 2 (2 self)
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Abstract. Radial Basis Function Neural Networks (RBFNNs) are well known because, among other applications, they present a good performance when approximating functions. The function approximation problem arises in the construction of a control system to optimize the process of the mineral reduction. In order to regulate the temperature of the ovens and other parameters, it is necessary a module to predict the final concentration of mineral that will be obtained from the source materials. This module can be formed by an RBFNN that predicts the output and by the algorithm that designs the RBFNN dynamically as more data is obtained. The design of RBFNNs is a very complex task where many parameters have to be determined, therefore, a genetic algorithm that determines all of them has been developed. This algorithm provides satisfactory results since the networks it generates are able to predict quite precisely the final concentration of mineral. 1
Output ValueBased Initialization for Radial Basis Function Neural Networks
, 2005
"... The use of Radial Basis Function Neural Networks (RBFNNs) to solve functional approximation problems has been addressed many times in the literature. When designing an RBFNN to approximate a function, the first step consists of the initialization of the centers of the RBFs. This initialization task ..."
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Cited by 2 (0 self)
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The use of Radial Basis Function Neural Networks (RBFNNs) to solve functional approximation problems has been addressed many times in the literature. When designing an RBFNN to approximate a function, the first step consists of the initialization of the centers of the RBFs. This initialization task is very important because the rest of the steps are based on the positions of the centers. Many clustering techniques have been applied for this purpose achieving good results although they were constrained to the clustering problem. The next step of the design of an RBFNN, which is also very important, is the initialization of the radii for each RBF. There are few heuristics that are used for this problem and none of them use the information provided by the output of the function, but only the centers or the input vectors positions are considered. In this paper, a new algorithm to initialize the centers and the radii of an RBFNN is proposed. This algorithm uses the perspective of activation grades for each neuron, placing the centers according to the output of the target function. The radii are initialized using the center’s positions and their activation grades so the calculation of the radii also uses the information provided by the output of the target function. As the experiments show, the performance of the new algorithm outperforms other algorithms previously used for this problem.
M.: MultiGridBased Fuzzy Systems for Function Approximation. LNCS/LNAI MICAI’2004
"... Abstract. In this paper we make use of a modified Grid Based Fuzzy System architecture, which may provide an exponential reduction in the number of rules needed. We also introduce an algorithm that automatically, from a set of given I/O training points, is able to determine the pseudooptimal archit ..."
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Abstract. In this paper we make use of a modified Grid Based Fuzzy System architecture, which may provide an exponential reduction in the number of rules needed. We also introduce an algorithm that automatically, from a set of given I/O training points, is able to determine the pseudooptimal architecture proposed as well as the optimal parameters needed (number and position of membership functions and fuzzy rule consequents). The suitability of the algorithm and the improvement in both performance and efficiency obtained are shown in an example. 1
Duroc and Iberian Pork Neural Network Classification by Visible and Near Infrared Reflectance Spectroscopy
 Journal of Food Engineering
, 2009
"... a b s t r a c t Visible and near infrared reflectance spectroscopy (VIS/NIRS) was used to differentiate between Duroc and Iberian pork in the M. masseter. Samples of Duroc (n = 15) and Iberian (n = 15) pig muscles were scanned in the VIS/NIR region (3502500 nm) using a portable spectral radiometer ..."
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a b s t r a c t Visible and near infrared reflectance spectroscopy (VIS/NIRS) was used to differentiate between Duroc and Iberian pork in the M. masseter. Samples of Duroc (n = 15) and Iberian (n = 15) pig muscles were scanned in the VIS/NIR region (3502500 nm) using a portable spectral radiometer. Both mutual information and VIS/NIRS spectra characterization were developed to generate a ranking of variables and the data were then processed by artificial neural networks, establishing 1, 3, or 10 wavelengths as input variable for classifying between the pig breeds. The models correctly classified >70% of all problem assumptions, with a correct classification of >95% for the threevariable assumption using either mutual information ranking or VIS/NIRS spectra characterization. These results demonstrate the potential value of the VIS/ NIRS technique as an objective and rapid method for the authentication and identification of Duroc and Iberian pork.