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91
ANFIS: AdaptiveNetworkBased Fuzzy Inference System”,
 IEEE Trans. on System, Man and Cybernetics,
, 1993
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Deterministic Annealing for Clustering, Compression, Classification, Regression, and Related Optimization Problems
 Proceedings of the IEEE
, 1998
"... this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, ph ..."
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Cited by 321 (20 self)
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this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, physics, biology, control and signal processing, information theory, complexity theory, and psychology (see [45]). Neural networks have provided a fertile soil for the infusion (and occasionally confusion) of ideas, as well as a meeting ground for comparing viewpoints, sharing tools, and renovating approaches. It is within the illdefined boundaries of the field of neural networks that researchers in traditionally distant fields have come to the realization that they have been attacking fundamentally similar optimization problems.
Functional Equivalence between Radial Basis Function Networks and Fuzzy Inference Systems
, 1993
"... This short article shows that under some minor restrictions, the functional behavior of radial basis function networks and fuzzy inference systems are actually equivalent. This functional equivalence implies that advances in each literature, such as new learning rules or analysis on representational ..."
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Cited by 169 (4 self)
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This short article shows that under some minor restrictions, the functional behavior of radial basis function networks and fuzzy inference systems are actually equivalent. This functional equivalence implies that advances in each literature, such as new learning rules or analysis on representational power, etc., can be applied to both models directly. It is of interest to observe that twomodels stemming from different origins turn out to be functional equivalent.
Growing radial basis neural networks: Merging supervised and unsupervised learning with network growth techniques
 IEEE Transactions on Neural Networks
, 1997
"... Abstract—This paper proposes a framework for constructing and training radial basis function (RBF) neural networks. The proposed growing radial basis function (GRBF) network begins with a small number of prototypes, which determine the locations of radial basis functions. In the process of training, ..."
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Cited by 58 (3 self)
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Abstract—This paper proposes a framework for constructing and training radial basis function (RBF) neural networks. The proposed growing radial basis function (GRBF) network begins with a small number of prototypes, which determine the locations of radial basis functions. In the process of training, the GRBF network grows by splitting one of the prototypes at each growing cycle. Two splitting criteria are proposed to determine which prototype to split in each growing cycle. The proposed hybrid learning scheme provides a framework for incorporating existing algorithms in the training of GRBF networks. These include unsupervised algorithms for clustering and learning vector quantization, as well as learning algorithms for training singlelayer linear neural networks. A supervised learning scheme based on the minimization of the localized classconditional variance is also proposed and tested. GRBF neural networks are evaluated and tested on a variety of data sets with very satisfactory results. Index Terms — Classconditional variance, network growing, radial basis neural network, radial basis function, splitting criterion,
Building Elementary Robot Skills from Human Demonstration
 In International Symposium on Intelligent Robotics Systems
, 1996
"... This paper presents a general approach to the acquisition of sensorbased robot skills from human demonstrations. Since humangenerated examples cannot be assumed to be optimal with respect to the robot, adaptation of the initially acquired skill is explicitly considered. Results for acquiring and r ..."
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Cited by 54 (6 self)
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This paper presents a general approach to the acquisition of sensorbased robot skills from human demonstrations. Since humangenerated examples cannot be assumed to be optimal with respect to the robot, adaptation of the initially acquired skill is explicitly considered. Results for acquiring and refining manipulation skills for a Puma 260 manipulator are given. 1 Introduction Since humans can carry out motions with no apparent difficulty, one would expect the generation of elementary skills to be a relatively simple problem. However, it turns out that it is extremely difficult to duplicate this elementary operative intelligence, which is used by humans unconsciously, in a computercontrolled robot [10]. This observation motivates research in the field of Robot Skill Acquisition via Human Demonstration [1, 11, 7], which is an extension of Robot Programming by Human Demonstration [9] that deals with the aquisition of sensorbased robot skills from human demonstrations (Fig. 1). Figure...
Face recognition with radial basis function (RBF) neural networks
 IEEE Transactions on Neural Networks
, 2002
"... Abstract—A general and efficient design approach using a radial basis function (RBF) neural classifier to cope with small training sets of high dimension, which is a problem frequently encountered in face recognition, is presented in this paper. In order to avoid overfitting and reduce the computati ..."
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Cited by 51 (2 self)
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Abstract—A general and efficient design approach using a radial basis function (RBF) neural classifier to cope with small training sets of high dimension, which is a problem frequently encountered in face recognition, is presented in this paper. In order to avoid overfitting and reduce the computational burden, face features are first extracted by the principal component analysis (PCA) method. Then, the resulting features are further processed by the Fisher’s linear discriminant (FLD) technique to acquire lowerdimensional discriminant patterns. A novel paradigm is proposed whereby data information is encapsulated in determining the structure and initial parameters of the RBF neural classifier before learning takes place. A hybrid learning algorithm is used to train the RBF neural networks so that the dimension of the search space is drastically reduced in the gradient paradigm. Simulation results conducted on the ORL database show that the system achieves excellent performance both in terms of error rates of classification and learning efficiency. Index Terms—Face recognition, Fisher’s linear discriminant, ORL database, principal component analysis, radial basis function (RBF) neural networks, small training sets of high dimension. I.
Combined Genetic Algorithm Optimization and Regularized Orthogonal Least Squares Learning for Radial Basis Function Networks
, 1999
"... The paper presents a twolevel learning method for radial basis function (RBF) networks. A regularized orthogonal least squares (ROLS) algorithm is employed at the lower level to construct RBF networks while the two key learning parameters, the regularization parameter and the RBF width, are optimiz ..."
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Cited by 40 (14 self)
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The paper presents a twolevel learning method for radial basis function (RBF) networks. A regularized orthogonal least squares (ROLS) algorithm is employed at the lower level to construct RBF networks while the two key learning parameters, the regularization parameter and the RBF width, are optimized using a genetic algorithm (GA) at the upper level. Nonlinear time series modeling and prediction is used as an example to demonstrate the effectiveness of this hierarchical learning approach.
Evaluation of Pattern Classifiers for Fingerprint and OCR Applications
 Pattern Recognition
, 1993
"... In this paper we evaluate the classification accuracy of four statistical and three neural network classifiers for two image based pattern classification problems. These are fingerprint classification and optical character recognition (OCR) for isolated handprinted digits. The evaluation results rep ..."
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Cited by 37 (2 self)
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In this paper we evaluate the classification accuracy of four statistical and three neural network classifiers for two image based pattern classification problems. These are fingerprint classification and optical character recognition (OCR) for isolated handprinted digits. The evaluation results reported here should be useful for designers of practical systems for these two important commercial applications. For the OCR problem, the KarhunenLo`eve (KL) transform of the images is used to generate the input feature set. Similarly for the fingerprint problem, the KL transform of the ridge directions is used to generate the input feature set. The statistical classifiers used were Euclidean minimum distance, quadratic minimum distance, normal, and knearest neighbor. The neural network classifiers used were multilayer perceptron, radial basis function, and probabilistic. The OCR data consisted of 7,480 digit images for training and 23,140 digit images for testing. The fingerprint data co...
Median Radial Basis Functions Neural Network
 IEEE Trans. on Neural Networks
, 1996
"... Radial Basis Functions (RBF) consists of a twolayer 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 ..."
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Cited by 34 (18 self)
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Radial Basis Functions (RBF) consists of a twolayer 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 Functions (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 histogrambased fast implementation is provided for the MRBF algorithm. The theoretical performance of the two training al...
An Efficient Method to Construct a Radial Basis Function Neural Network Classifier
, 1997
"... Radial basis function neural network(RBFN) has the power of the universal function approximation. But it is usually not straightforward how to construct an RBFN to solve a given problem. This paper describes a method to construct an RBFN classifier efficiently and effectively. The method determines ..."
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Cited by 31 (1 self)
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Radial basis function neural network(RBFN) has the power of the universal function approximation. But it is usually not straightforward how to construct an RBFN to solve a given problem. This paper describes a method to construct an RBFN classifier efficiently and effectively. The method determines the middle layer neurons by a fast clustering algorithm and computes the optimal weights between the middle and the output layers statistically. We applied the proposed method to construct an RBFN classifier for an unconstrained handwritten digit recognition. The experiment showed that the method could construct an RBFN classifier fast and the performance of the classifier was better than the best result previously reported. Keyword : Radial Basis Function, Linear Discriminant Function, Classification, APCIII, Clustering, GRBF, LMS, Handwritten Digit Recognition RBF Neural Network Classifier 2 1 INTRODUCTION Radial basis function neural network(RBFN) (Moody and Darken, 1989; Poggio and G...