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 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 lower-dimensional 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.

Abstract: Matching Pursuit algorithms learn a function that is a weighted sum of basis functions, by sequentially appending functions to an initially empty basis, to approximate a target function in the least-squares sense. We show how matching pursuit can be extended to use non-squared error loss functions, and how it can be used to build kernel-based solutions to machine learning problems, while keeping control of the sparsity of the solution. We present a version of the algorithm that makes an optimal choice of both the next basis and the weights of all the previously chosen bases. Finally, links to boosting algorithms and RBF training procedures, as well as an extensive experimental comparison with SVMs for classification are given, showing comparable results with typically much sparser models.

Abstract: Many types of radial basis functions, such as multiquadrics, contain a free parameter In the limit where the basis functions become increasingly flat, the linear system to solve becomes highly ill-conditioned, and the expansion coefficients diverge Nevertheless, we find in this study that limiting interpolants often exist and take the form of polynomials In the 1-D case, we prove that with simple conditions on the basis function, the interpolants converge to the Lagrange interpolating polynomial Hence, differentiation of this limit is equivalent to the standard finite difference method We also summarize some preliminary observations regarding the limit in 2-D

Abstract: Sets of multivariable functions are described for which worst case errors in linear approximation are larger than those in approximation by neural networks. A theoretical framework for such a description is developed in the context of nonlinear approximation by fixed versus variable basis functions. Comparisons of approximation rates are formulated in terms of certain norms tailored to sets of basis functions. The results are applied to perceptron networks.

Abstract: A complex radial basis function neural network is proposed for equalization of quadrature amplitude modulation (QAM) signals in communication channels. The network utilizes a sequential learning algorithm referred to as complex minimal resource allocation network (CMRAN) and is an extension of the MRAN algorithm originally developed for online learning in real-valued radial basis function (RBF) networks. CMRAN has the ability to grow and prune the (complex) RBF network's hidden neurons to ensure a parsimonious network structure. The performance of the CMRAN equalizer for nonlinear channel equalization problems has been evaluated by comparing it with the functional link artificial neural network (FLANN) equalizer of J.C. Patra et al. (1999) and the Gaussian stochastic gradient (SG) RBF equalizer of I. Cha and S. Kassam (1995). The results clearly show that CMRANs performance is superior in terms of symbol error rates and network complexity.

Abstract: Compactly supported radial basis functions (CS-RBFs) have been recently introduced in the context of the dual reciprocity method as a possible cure of dense matrices and ill-conditioning problems when using the classical radial basis functions. However, the support scaling factor and slow convergence rate of the CS-RBFs have also raised issues on the effectiveness of the CS-RBFs. In this paper, two multilevel schemes have been proposed to alleviate these problems.

Abstract: This paper proposes a new Model Predictive Control scheme incorporating a Radial Basis Function Network Observer for the fuel injection problem. Two new contributions are presented here. First a Radial Basis Function Network is used as an observer for the air system. This allows for gradual adaptation of the observer, ensuring the control scheme is capable of maintaining good performance under changing engine conditions brought about by engine wear, variations between individual engines, and other similar factors. The other major contribution is the use of model predictive control algorithms to compensate for the fuel pooling effect on the intake manifold walls. Two model predictive control algorithms are presented which enforce input, and input and state constraints. In this way stability under the constraints is guaranteed. A comparison between the two constrained MPC algorithms is qualitatively presented, and conclusions are drawn about the necessity of constraints for the fuel injection problem. Simulation results are presented that demonstrate the effectiveness of the control scheme, and the proposed control ap-proach is validated on a four-cylinder spark ignition engine.

Abstract: In radial basis function (RBF) networks, placement of centers is said to have a significant effect on the performance of the network. Supervised learning of center locations in some applications show that they are superior to the networks whose centers are located using unsupervised methods. But such networks can take the same training time as that of sigmoid networks. The increased time needed for supervised learning offsets the training time of regular RBF networks. One way to overcome this may be to train the network with a set of centers selected by unsupervised methods and then to fine tune the locations of centers. This can be done by first evaluating whether moving the centers would decrease the error and then, depending on the required level of accuracy, changing the center locations. This paper provides new results on bounds for the gradient and Hessian of the error considered first as a function of the independent set of parameters, namely the centers, widths, and weights; and then as a function of centers and widths where the linear weights are now functions of the basis function parameters for networks of fixed size. Moreover, bounds for the Hessian are also provided along a line beginning at the initial set of parameters. Using these bounds, it is possible to estimate how much one can reduce the error by changing the centers. Further to that, a step size can be specified to achieve a guaranteed, amount of reduction in error.

Abstract: This paper presents a novel and interesting combination of wavelet techniques and eigenfaces to extract features for face recognition. Eigenfaces reduce the dimensions of face vectors while wavelets reveal information that is unavailable in the original image. Extensive experiments have been conducted to test the new approach on the ORL face database, using a radial basis function neural network classifier. The results of the experiments are encouraging and the new approach is a step forward in face recognition.

Abstract: This paper compares the performances of a multilayer perceptron network (MLPN) and a radial basis function network (RBFN) for the online identification of the nonlinear dynamics of a synchronous generator. Deviations of signals from their steady state values are used. The computational complexity required to process the data for online training, generalization and online global minimum testing are investigated by time-domain simulations. The simulation results show that, compared to the MLPN, the RBFN is simpler to implement, needs less computational memory, converges faster and global minimum convergence is achieved even when operating conditions change.

Abstract: A novel approach for applying genetic algorithms to the configuration of radial basis function networks is presented. A new crossover operator that allows for some control over the competing conventions problem is introduced. Also, a minimalist initialization scheme which tends to generate more parsimonious models is also presented. Finally, a reformulation of generalized cross-validation criterion for model selection, making it more conservative, is discussed. The proposed model is submitted to a computational experiment in order to verify its effectiveness.

Abstract: Summary Neural models for computing the resonant frequency of electrically thin and thick circular microstrip antennas, based on the multilayered perceptrons and the radial basis function networks, are presented. Five learning algorithms, delta-bar-delta, extended delta-bar-delta, quick-propagation, directed random search and genetic algorithms, are used to train the multilayered perceptrons. The radial basis function network is trained according to its learning strategy. The resonant frequency results of neural models are in very good agreement with the experimental results available in the literature. In this paper, the characteristic impedance and the effective permittivity of the asymmetric coplanar waveguide backed with a conductor are also computed by using only one neural model trained by the backpropagation with momentum and the extended delta-bar-delta algorithms. When the performances of neural models are compared with each other, the best results for test are obtained from the multilayered perceptrons trained by the extended delta-bar-delta algorithm.

Abstract: Robust control techniques such as sliding mode control (SMC) require a dynamic model of the plant and bounds on modeling uncertainty to formulate control laws with guaranteed stability. Although techniques for modeling dynamic systems and estimating model parameters are well established, very few procedures exist for estimating uncertainty bounds. In the case of SMC design, a conservative global bound is usually chosen to ensure closed-loop stability over the entire operating space. The primary drawbacks of this conservative, "hard computing" approach are excessive control activity and reduced performance, particularly in regions of the operating space where the model is accurate. In this paper, a novel approach to estimating uncertainty bounds for dynamic systems is introduced. This "soft computing" approach uses a unique artificial neural network, the 2-Sigma network, to bound modeling uncertainty adaptively. This fusion of intelligent uncertainty bound estimation with traditional SMC results in a control algorithm that is both robust and adaptive. Simulations and experimental demonstrations conducted on a magnetic levitation system confirm these capabilities and reveal excellent tracking performance without excessive control activity.

Abstract: A method and apparatus are disclosed for classifying objects using a hierarchical object classification scheme. The hierarchical object classification scheme provides candidate classes with an increasing degree of specificity as the hierarchy is traversed from the root node to the leaf nodes. Each node in the hierarchy has an associated classifier, such as a Radial Basis Function classifier, that determines a probability that an object is a member of the class associated with the node. The nodes of the hierarchical tree are individually trained by any learning technique, such as the exemplary Radial Basis Function Network, that uses appearance-based information of the objects under consideration to classify objects. A disclosed recognition scheme uses a decision criterion based upon recognition error to classify objects.

Abstract: We present a meshless method based on thin plate radial basis function method for the numerical solution of advection-diffusion equation, which has been a long standing problem. The efficiency of the method in terms of computational processing time, accuracy and stability is discussed. The results are compared with the findings from the finite difference methods as well as the analytical solution. Our analysis shows that the radial basis functions method, with its simple implementation, generates excellent results and speeds up the computational processing time, independent of the shape of the domain and irrespective of the dimension of the problem.

Abstract: In this paper we propose the idea of building a new software reliability models using Radial Basis Function (RBF) network. The RBF network is easy to design and the network structure can be represented in a simple mathematical equation. Our goal is to build a generalized model that can be used for software predication [1]. The RBF network was trained with a set of data collected from the testing process of Military application projects. The RBF model was tested on other sets of projects. The results are promising.

Abstract: This paper discusses an implementation and application of Radial Basis Function (RBF) Networks. This type of neural networks performs a universal approach to function approximation. The same algorithm and program may be successfully applied to regression modeling or pattern classification. We illustrate the most important characteristics of RBF networks with a number of examples and discuss network behavior in depth. The software has been implemented in the A+ language, which became available to developers in January of 2001.

Abstract: The paper presents a novel approach for developing simulation metamodels using Gaussian radial basis functions. This approach is based on some recently developed mathematical results for radial basis functions. It is systematic, explicitly controls the underfitting and overfitting tradeoff, and uses a fast computational algorithm that requires minimal human involvement. This approach is illustrated by developing metamodels for the M/M/1 queueing system.

Abstract: This paper presents a machining error compensation methodology using an Artificial Neural Network (ANN) model trained by an inspection database of the On-Machine-Measurement (OMM) system. This is an application of the CAD/CAM/CAI integration concept. First, to improve machining and inspection accuracies, the geometric errors of a three-axis CNC machining centre and the probing errors are compensated using a closed-loop configuration. Then, a workpiece is machined using the machining centre, and the error distributions of the machined surface are inspected using OMM. In order to analyse efficiently the machining errors, two characteristic error parameters, W err and D err , are defined. Subsequently, these parameters are modelled using a Radial Basis Function (RBF) network approach as an ANN model. Based on the RBF network model, the tool path is corrected to effectively reduce the errors using an iterative algorithm. In the iterative algorithm, the changes of the cutting conditions can be identified accor...