Abstract: An adaptive control technique, using dynamic structure Gaussian radial basis function neural networks, that grow in time according to the location of the system's state in space is presented for the affine class of nonlinear systems having unknown or partially known dynamics. The method results in a network that is "economic" in terms of network size, for cases where the state spans only a small subset of state space, by utilizing less basis functions than would have been the case if basis functions were centered on discrete locations covering the whole, relevant region of state space. Additionally, the system is augmented with sliding control so as to ensure global stability if and when the state moves outside the region of state space spanned by the basis functions, and to ensure robustness to disturbances that arise due to the network inherent approximation errors and to the fact that for limiting the network size, a minimal number of basis functions are actually being used. Adaptation laws and sliding control gains that ensure system stability in a Lyapunov sense are presented, together with techniques for determining which basis functions are to form part of the network structure. The effectiveness of the method is demonstrated by experiment simulations.

Abstract: Radial basis functions (RBFs) consist of a two-layer 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 function (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 histogram-based fast implementation is provided for the MRBF algorithm. The theoretical performance of the two training algorithms is comparatively evaluated when estimating the network weights. The network is applied in pattern classification problems and in optical flow segmentation.

Abstract: The efficiency of the orthogonal least squares (OLS) method for training approximation networks is examined using the criterion of energy compaction. We show that the selection of basis vectors produced by the procedure is not the most compact when the approximation is performed using a nonorthogonal basis. Hence, the algorithm does not produce the smallest possible networks for a given approximation error. Specific examples are given using the Gaussian radial basis functions type of approximation networks.

Abstract: In modelling rainfall-runoff and flows in drainage systems it can be advantageous to adopt a neural network (NN). Unfortunately traditional NN learning procedures such as back-propagation can be very slow and expensive to carry out. However, if radial basis function (RBF) networks are adopted with radial centres fixed by a suitable data clustering technique then good results may be obtained very much more rapidly. RBF networks are here shown to be very effective in modelling runoff for a large rainfall database and to give broadly comparable results to those obtained by fine-tuning the much slower back-propagation procedure. The specific model is based on the assumption that runoff depends on time, rainfall intensity I, the rate of change of I and the integral of I.

Abstract: Studies convergence properties of radial basis function (RBF) networks for a large class of basis functions, and reviews the methods and results related to this topic. The authors obtain the network parameters through empirical risk minimization. The authors show the optimal nets to be consistent in the problem of nonlinear function approximation and in nonparametric classification. For the classification problem the authors consider two approaches: the selection of the RBF classifier via nonlinear function estimation and the direct method of minimizing the empirical error probability. The tools used in the analysis include distribution-free nonasymptotic probability inequalities and covering numbers for classes of functions.

Abstract: The paper presents experiments using a radial basis function (RBF) network to tackle the unconstrained face recognition problem using low resolution video information. Input representations that mimic the effects of receptive field functions found at various stages of the human vision system were used with RBF network; that learnt to classify and generalise over different views of each person to be recognised. In particular, Difference of Gaussian (DoG) filtering and Gabor wavelet analysis are compared for face recognition from an image sequence. RBF techniques are shown to provide excellent levels of performance where the view varies and the authors discuss how to relax constraints on data capture and improve preprocessing to obtain an effective scheme for real-time, unconstrained face recognition.

Abstract: This paper describes the development of a control system to support an automated parking mode in driving passenger cars. By using recent advances in the artificial neural network technology and a combination of linear feedback and nonlinear feedforward control, we propose a novel architecture for the parking motion controller. The paper presents the results of the controller design and analysis, including parking problem analysis, stability analysis for the feedback controller, formulation and optimal solution of the parking trajectory planning problem, and design of a parking motion planning architecture based on a radial basis function network. Two general cases of backward parking considered in this work are emulated using the proposed controller. The emulation results reveal high efficiency of the presented approach and demonstrate that the proposed system can be implemented on a typical passenger car.

Abstract: The paper describes a condition-monitoring scheme based on first principles models the scheme involves estimating the values of model parameters that are expected to change in the event of a fault. The first principles models are, in general, not linear in the parameters, and recursive estimation of the parameters of these models is avoided by estimating the parameters of an intermediate model that is linear in the parameters. This intermediate model, which takes the form of a radial basis function network, is used periodically to generate data covering the complete operating range of the system. These data are then used in the estimation of the parameters of the first principles model. The paper describes the techniques used and presents results from applying the method to the task of detecting two faults in the cooling coil subsystem of an air-handling unit.

Abstract: This paper presents experiments using an adaptive learning compo nent based on Radial Basis Function RBF networks to tackle the unconstrained face recognition problem using low resolution video in formation Firstly we performed preprocessing of face images to mimic the e ects of receptive eld functions found at various stages of the hu man vision system These were then used as input representations to RBF networks that learnt to classify and generalise over di erent views for a standard face recognition task Two main types of preprocessing Di erence of Gaussian ltering and Gabor wavelet analysis are com pared Secondly we provide an alternative face unit RBF network model that is suitable for large scale implementations by decomposi tion of the network which avoids the unmanagability of neural net works above a certain size Finally we show the D shift scale and y axis rotation invariance properties of the standard RBF network Quantitative and qualitative di erences in these schemes are described and conclusions drawn about the best approach for real applications to address the face recognition problem using low resolution images

Abstract: We investigate a technique for image restoration using nonlinear networks based on radial basis functions. The technique is also based on the concept of training or learning by examples. When trained properly, these networks are used as spatially invariant feedforward nonlinear filters that can perform restoration of images degraded by nonlinear degradation mechanisms. We examine a number of network structures including the Gaussian radial basis function network (RBFN) and some extensions of it, as well as a number of training algorithms including the stochastic gradient (SG) algorithm that we have proposed earlier. We also propose a modified structure based on the Gaussian-mixture model and a learning algorithm for the modified network. Experimental results indicate that the radial basis function network and its extensions can be very useful in restoring images degraded by nonlinear distortion and noise.

Abstract: We have developed a radial basis function network (RBFN) for visual autonomous road following. Preliminary testing of the RBFN was done using a driving simulator, and the RBFN was then installed on an actual vehicle at Carnegie Mellon University for testing in an outdoor road-following application. In our first attempts, the RBFN had some success, but it experienced some significant problems such as jittery control and driving failure. Several improvements have been made to the original RBFN architecture to overcome these problems in simulation and more importantly in actual road following, and the improvements are described in this paper.

Abstract: This paper presents a comparison between two Artificial Neural Network (ANN) approaches, namely, Multilayer Perceptron (MLP) and Radial Basis Function (RBF) networks, in flood forecasting. The basic difference between the two methods is that the parameters of the former network are nonlinear and those of the latter are linear. The optimum model parameters are therefore guaranteed in the latter, whereas it is not so in the more popularly adopted former approach. The two methods are applied to predict water levels at stations in an experimental drainage basin and in a major river in China during storm periods. The RBF network based models give predictions comparable in accuracy to those from the MLP based models. It is also observed that the RBF approach requires less time for model development since no repetition is required to reach the optimum model parameters.

Abstract: Historical information on credit card transactions can be used to generate a fraud score which can then be used to reduce credit card fraud. The report describes a fraud-nonfraud classification methodology using a radial basis function network (RBFN) with a density based clustering approach. The input data is transformed into the cardinal component space and clustering as well as RBFN modeling is done using a few cardinal components. The methodology has been tested on a fraud detection problem and the preliminary results obtained are satisfactory.

Abstract: The principle of F-projection, in sequential function estimation, provides a theoretical foundation for a class of gaussian radial basis function networks known as the resource allocating networks (RAN). The ad hoc rules for adaptively changing the size of RAN architectures can be justified from a geometric growth criterion defined in the function space. In this paper, we show that the same arguments can be used to arrive at a pruning with replacement rule for RAN architectures with a limited number of units. We illustrate the algorithm on the laser time series prediction problem of the Santa Fe competition and show that results similar to those of the winners of the competition can be obtained with pruning and replacement.

Abstract: We discuss the application of a radial basis function (RBF) network to the channel equalization problem. In particular, the purpose of the paper is to improve the previously developed RBF equalizer with training using K-means and LMS methods; reducing the RBF network size by considering a lesser number of RBF centers, and developing new techniques for determining channel order which is required to specify the structure of an RBF equalizer. A linear regression model was used for estimating the channel order. The basic idea of reducing the network size is to select the centers, based on the channel lag. This work includes the comparison of the limits of mean square error (MSE) convergence of both a linear equalizer and an RBF equalizer.

Abstract: Four artificial neural network paradigms (multilayer perceptron networks, learning vector quantization networks, and radial and asymmetric basis function networks) and two statistical methods (parametric statistical classification by modelling each class with Gaussian distributions, and non-parametric density estimation via the K-nearest neighbour method) were compared for their ability to identify seven freshwater and five marine phytoplankton species from flow cytometric data. Kohonen self-organizing maps were also used to examine similarities between species. Optimized networks and statistical methods performed similarly, correctly identifying between 86.8% and 90.1% of data from freshwater species, and between 81.3% and 84.1% of data from marine species. Choice of identification technique must therefore be made on the basis of other criteria. We highlight the way each method partitions the data space and thereby separates the data clusters, and discuss the relative merits of each with reference to complexity of data boundaries, training time, analysis time and behaviour when presented with 'novel' data.

Abstract: This paper proposes a new neural network model called radial basis probabilistic neural network (RBPNN) based on the radial basis function network (RBFN) and the probabilistic neural network (PNN). This new model inherits the merits of the two old models and tries to avoid their defects. Finally, the experimental results show that this new model is effective and practical.

Abstract: This paper describes a neural network for approximation problems on the sphere. The von Mises basis function is introduced, whose activation depends on polar rather than Cartesian input coordinates. The architecture of the von Mises Basis Function (VMBF) neural network is presented along with the corresponding gradient-descent learning rules. The VMBF neural network is used to solve a particular spherical problem of approximating acoustic parameters used to model perceptual auditory space. This model ultimately serves as a signal processing engine to synthesize a virtual auditory environment under headphone listening conditions. Advantages of the VMBF over standard planar Radial Basis Functions (RBFs) are discussed.

Abstract: A hybrid algorithm for determining Radial Basis Function (RBF) networks is proposed. Evolutionary learning is applied to the non-linear problem of determining RBF network architecture (number of hidden layer nodes, basis function centres and widths) in conjunction with supervised gradient-based learning for tuning connection weights. A direct encoding of RBF hidden layer node basis function centres and widths is employed. The genetic operators utilised are adapted from those used in recent work on evolution of fuzzy inference systems. A parsimonious allocation of training sets and training epochs to evaluation of candidate networks during evolution is proposed in order to accelerate the learning process.

Abstract: In this paper, we compare the capabilities of various forms of radial basis function networks as nonlinear short-term predictors for speech signals representing sustained utterances of German vowels. We use RBF and RBF-AR1 network architectures, trained using a standard algorithm or alternatively the extended Kalman filter (EKF) algorithm, and linear least squares predictors. We also look at cascaded forms of linear/nonlinear predictors. We evaluate both prediction gain and spectral flatness measure of the residual. The results indicate: The RBF-AR structure is the most powerful, EKF training yields better results than standard training for RBF networks, and a non-cascaded RBF-AR predictor produces results superior to cascaded predictors.

Abstract: Radial basis function networks can be trained quickly using linear optimisation once centres and other associated parameters have been initialised. The authors propose a small adjustment to a well accepted initialisation algorithm which improves the network accuracy over a range of problems. The algorithm is described and results are presented.

Abstract: We introduce a local adaptation process in the orthogonal least squares (OLS) learning algorithm for the selection of radial basis function (RBF) networks. Using simulation results, we show that the proposed algorithm can find significantly better subset models than the OLS algorithm.

Abstract: This paper considers a problem of nonholonomic motion planning. A practical paradigm for planning and stabilization of motion in a class of multivariate nonlinear (nonholonomic) systems is presented and applied to a planar free-floating manipulator system. The controller architecture designed in the paper is based on the radial basis function approximation of an optimal control program for any desired motion. This architecture also incorporates a sampled-data feedback stabilization algorithm. The proposed control technique overcomes certain problems associated with other control approaches available for nonholonomic systems. The presented simulation results reveal a promising potential of the proposed control paradigm. This paradigm can be extended to a broader class of nonlinear control problems.