Abstract: From the Publisher: "In many areas of mathematics, science and engineering, from computer graphics to inverse methods to signal processing it is necessary to estimate parameters, usually multidimensional, by approximation and interpolation. Radial basis functions are a modern and powerful tool which work well in very general circumstances, and so are becoming of widespread use, as the limitations of other methods, such as least squares, polynomial interpolation or wavelet-based, become apparent." This is the first book devoted to the subject and the author's aim is to give a thorough treatment from both the theoretical and practical implementation viewpoints. For example, he emphasises the many positive features of radial basis functions such as the unique solvability of the interpolation problem, the computation of interpolants, their smoothness and convergence, and provides a careful classification of the radial basis functions into types that have different convergence. A comprehensive bibliography rounds off what will prove a very valuable work.

Abstract: In recent years, artificial neural networks (ANNs) have been applied to forecasting in many areas of engineering. In this note, a sequentially adaptive radial basis function network is applied to the forecasting of reference evapotranspiration (ETo). The sequential adaptation of parameters and structure is achieved using an extended Kalman filter. The criterion for network growing is obtained from the Kalman filter’s consistency test, while the criteria for neuron/connection pruning are based on the statistical parameter significance test. The weather parameter data (air temperature, relative humidity, wind speed, and sunshine) were available at Nis, Serbia and Montenegro, from January 1977 to December 1996. The monthly reference evapotranspiration data were obtained by the Penman-Monteith method, which is proposed as the sole standard method for the computation of reference evapotranspiration. The network learned to forecast ETo,t+1 based on ETo,t-11 and ETo,t-23. The results show that ANNs can be used f...

Abstract: In this paper a neural network for solving partial differential equations (PDE) is described The activation functions of the hidden nodes are the radial basis functions (RBF) whose parameters are learnt by a two-stage gradient descent strategy A new growing radial basis functions-node insertion strategy with different radial basis functions is used in order to improve the net performances The learning strategy is able to save computational time and memory space because of the selective growing of nodes whose activation functions consist of different radial basis functions An analysis of the learning capabilities and a comparison of the net performances with other approaches have been performed It is shown that the resulting network improves the approximation results

Abstract: Presents a systematic approach for constructing reformulated radial basis function (RBF) neural networks, which was developed to facilitate their training by supervised learning algorithms based on gradient descent. This approach reduces the construction of radial basis function models to the selection of admissible generator functions. The selection of generator functions relies on the concept of the blind spot, which is introduced in the paper. The paper also introduces a new family of reformulated radial basis function neural networks, which are referred to as cosine radial basis functions. Cosine radial basis functions are constructed by linear generator functions of a special form and their use as similarity measures in radial basis function models is justified by their geometric interpretation. A set of experiments on a variety of datasets indicate that cosine radial basis functions outperform considerably conventional radial basis function neural networks with Gaussian radial basis functions. Cosine radial basis functions are also strong competitors to existing reformulated radial basis function models trained by gradient descent and feedforward neural networks with sigmoid hidden units.

Abstract: A hybrid neuro-symbolic problem solving model is presented in which the aim is to forecast parameters of a complex and dynamic environment in an unsupervised way. In situations in which the rules that determine a system are unknown, the prediction of the parameter values that determine the characteristic behaviour of the system can be a problematic task. The system employs a case-based reasoning model to wrap a growing cell structures network, a radial basis function network and a set of Sugeno fuzzy models to provide an accurate prediction. Each of these techniques is used in a different stage of the reasoning cycle of the case-based reasoning system to retrieve, adapt and review the proposed solution to the present problem. This system has been used to predict the red tides that appear in the coastal waters of the north west of the Iberian Peninsula. The results obtained from experiments are presented.

Abstract: This paper proposes a generic criterion that defines the optimum number of basis functions for radial basis function (RBF) neural networks. The generalization performance of an RBF network relates to its prediction capability on independent test data. This performance gives a measure of the quality of the chosen model. An RBF network with an overly restricted basis gives poor predictions on new data, since the model has too little flexibility (yielding high bias and low variance). By contrast, an RBF network with too many basis functions also gives poor generalization performance since it is too flexible and fits too much of the noise on the training data (yielding low bias but high variance). Bias and variance are complementary quantities, and it is necessary to assign the number of basis function optimally in order to achieve the best compromise between them. In this paper we use Stein's unbiased risk estimator to derive an analytical criterion for assigning the appropriate number of basis functions. Two cases of known and unknown noise have been considered and the efficacy of this criterion in both situations is illustrated experimentally. The paper also shows an empirical comparison between this method and two well known classical methods, cross validation and the Bayesian information criterion, BIC.

Abstract: This paper is studying a solar-array modelling and maximum power point tracking by comparing 2 neural networks which are back-propagation neural network and radial basis function neural network. Neural network has the potential to provide an improved method of deriving nonlinear models which is complementary to conventional techniques. The performance of the models and predicted maximum power point of solar cell are evaluated by comparing it with that of the conventional model by simulation. The simulation results has shown that both neural network work very well. In addition, the simulation results have shown that training for back-propagation takes longer time than radial basis function. However, back-propagation neural network needs less information for training. Radial basis function needs more information in order to get accurate modelling.

Abstract: Classifying the structure of protein is a very important task in biological data By means of the classification, the relationships and characteristics among known proteins can be exploited to predict the structure of new proteins The study of the protein structures is based on the sequences and their similarity It is a difficult task Recently, due to the ability of machine learning techniques, many researchers have applied them to probe into this protein classification problem We also apply here machine learning methods for multi-class protein fold recognition problem by proposing a novel hierarchical learning architecture This novel hierarchical learning architecture can be formed by NN (neural networks) or SVM (support vector machine) as basic building blocks Our results show that both of them can perform well We use this new architecture to attack the multi-class protein fold recognition problem as proposed by Dubchak and Ding in 2001 With the same set of features our method can not only obtain better prediction accuracy and lower computation time, but also can avoid the use of the stochastic voting process in the original approach

Abstract: Feature selection and architecture optimization are two key tasks in most neural network applications. Appropriate input features must be selected from a given (and often large) set of possible features and architecture parameters of the network such as the number of hidden neurons or learning parameters must be adapted with respect to the selected features and a learning data set. This article sets out an evolutionary algorithm (EA) that performs the tasks simultaneously for radial basis function (RBF) networks. The feasibility and the benefits of this approach are demonstrated in an application in the area of computer security: the detection of attacks (intrusive behavior) in computer networks. The EA, however, is independent from the application example given so that the ideas and solutions may easily be transferred to other applications and even other neural network paradigms. In the application example investigated overall classification rates of about 99.4% (average of eight attack types) can be reached for independent validation data.

Abstract: We propose an improved version of the normal k-means clustering algorithm to select the hidden layer neurons of a radial basis function (RBF) neural network. The normal k-means algorithm has been modified to capture more knowledge about the distribution of input patterns and to take care of hyper-ellipsoidal shaped clusters. The RBF neural network with the proposed algorithm has been tested with three different machine-learning data sets. The average recognition rate of an RBF neural network over these data sets has been found to be 93.70% using the proposed improved k-means algorithm, whereas in the method using the normal k-means algorithm, the corresponding value is found to be 88.12%. Clearly, the results show that the performance of the RBF neural network using the proposed modified k-means algorithm has been improved.

Abstract: The conventional transient stability measure of power system robustness to withstand large disturbances is usually named critical clearing time (CCT). The CCT evaluation involves elaborate computations that often include time-consuming solutions of nonlinear on-fault system equations. Among several approaches that have been proposed in the literature to meet very stringent needs of transient stability analysis, recent works suggest that artificial neural networks (ANNs) may be particularly appropriate. In this work, we propose the use of a radial basis function network (RBFN) for estimating the CCT of single faults in power systems. The proposed method has been applied for online transient stability analysis of a small power system (45 buses, 72 lines and/or transformers, and 10 generators). For RBFNs training purposes, we used 19 contingencies with 800 stability scenarios each. For verifying the RBFNs global performance, it was analysed the RBFN sensitivity with respect to the neuron numbers in hidden layer (25, 50, 75, and 100 neurons) for a set of 100 test cases. The numerical results provide a very good global performance index (mean relative error lesser than 3.65%).

Abstract: Electrocardiogram (ECG) is a nonstationary signal; therefore, the disease indicators may occur at random in the time scale. This may require the patient be kept under observation for long intervals in the intensive care unit of hospitals for accurate diagnosis. The present study examined the classification of the states of patients with certain diseases in the intensive care unit using their ECG and an Artificial Neural Networks (ANN) classification system. The states were classified into normal, abnormal and life threatening. Seven significant features extracted from the ECG were fed as input parameters to the ANN for classification. Three neural network techniques, namely, back propagation, self-organizing maps and radial basis functions, were used for classification of the patient states. The ANN classifier in this case was observed to be correct in approximately 99% of the test cases. This result was further improved by taking 13 features of the ECG as input for the ANN classifier.

Abstract: Over the past few years, security has been an increasing concern, with the growth of network and technological development. An intrusion detection system is a critical component for secure information management. Unfortunately, present IDS's falls short of providing protection required for growing concern. Creation of an IDS to detect anomaly intrusions, in a timely and accurate manner, has been an elusive goal for researchers. This paper describes a host-based IDS model, utilizing a Radial Basis Function neural network. It functions as a combined anomaly/misuse detector that helps to overcome most of the limitations in existing models. Rather than creating user profiles or behavioral characteristics, we trained our network using session data in the identification and tested experimentally on different attack/normal sessions. These results suggest that training the IDS on session data is not only effective in detecting intrusions, but also accurate and timely.

Abstract: In this paper, a face recognition algorithm using multi feature and Radial basis Function Network (RBFN) is proposed. The algorithm consists of three steps. In the first step, a coarse classification is performed using Fourier frequency spectrum feature, and only the first k gallery images with minimum Euclidean distance to the probe image are retained. In the second step, the Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) features of frequency spectrum are extracted, which will be taken as the input of the RBFN in the third step. In the last step, the classification is carried out by using RBFN. The proposed approach has been tested on ORL face database and Shimon database. The experimental results have demonstrated that the performance of this algorithm is much superior to the other algorithms on the same database.

Abstract: A two-step learning scheme for radial basis function neural networks (RBFNN) is proposed. A genetic algorithm initially optimises the parameters of the RBFNN and a hybrid learning algorithm adjusts these parameters further. The designed network is not only parsimonious but also has better generalisation performance.

Abstract: This paper presents a new model of an artificial neural network solving classification problems, called Local Transfer Function Classifier (LTF-C). Its architecture is very similar to this of the Radial Basis Function neural network (RBF), however it utilizes an entirely different learning algorithm. This algorithm is composed of four main parts: changing positions of reception fields, changing their sizes, insertion of new hidden neurons and removal of unnecessary ones during the training. The paper presents also results of LTF-C application to three real-life tasks: handwritten digit recognition, credit approval and cancer diagnosis. LTF-C was able to solve each of these problems with better accuracy than most popular classification systems. Moreover, LTF-C was relatively small and fast.

Abstract: With the rapidly increasing impact of the Internet, the development of appropriate intrusion detection systems (IDS) gains more and more importance. This article presents a performance comparison of four neural and fuzzy paradigms (multilayer perceptrons, radial basis function networks, NEFCLASS systems, and classifying fuzzy-k-means) applied to misuse detection on the basis of TCP and IP header information. As an example, four different attacks (Nmap, Portsweep, Dict, Back) will be detected utilising evaluation data provided by the Defense Advanced Research Projects Agency (DARPA). The best overall classification results (99.42%) can be achieved with radial basis function networks, which model hyperspherical clusters in the feature space.

Abstract: In this paper we propose several sets of new features for protein fold prediction. The first feature set consisting of 47 features uses only the sequence information. We also define four different sets of features based on hydrophobicity of amino acids. Each such set has 400 features which are motivated by folding energy modeling. To define these features we have considered pair-wise amino acids (AA) interaction potential. The effectiveness of the proposed feature sets is tested using multilayer perceptron and radial basis function networks to solve the 4 class (level 1) and 27 class (level 2) prediction problems as defined in the context of SCOP classification. Our investigation shows that such features have good discriminating powers in predicting protein folds.

Abstract: We propose a test for neglected nonlinearity that uses an alternative artificial neural network (ANN) specification to the one commonly used in the literature. We use radial basis functions for the ‘hidden layer’ with basis function centres and radii chosen from the sample data set and selected on the basis of an information criterion. The procedure is straightforward to implement and outperforms, in many cases, the ANN test proposed by Lee et al. (1993) and the analytic variation devised by Terasvirta et al. (1993).

Abstract: Minimising the number of bits per connection weight in hardware realisation of a radial basis function neural network (RBFNN) will result in high-speed and low-cost implementation, with possible increase in output error. A weight quantisation accuracy selection method is proposed, to find an appropriate number of bits for a given stochastic sensitivity measure, which quantifies the relationship between the variance of the output error and first- and second-order statistics of input, weight and their perturbations.

Abstract: In this paper, we investigate the use of radial basis functions for solving Poisson problems with a near-singular inhomogeneous source term. The solution of the Poisson problem is first split into two parts: near-singular solution and smooth solution. A method for evaluating the near-singular particular solution is examined. The smooth solution is further split into a particular solution and a homogeneous solution. The MPS-DRM approach is adopted to evaluate the smooth solution. Copyright © 2003 John Wiley & Sons, Ltd.

Abstract: Radial Basis Function Networks (RBFNs) Gaussian Radial Basis Function Neural Networks Learning Algorithms for Gaussian RBF Neural Networks Concluding Remarks Problems ]]>

Abstract: This paper establishes weak and strong universal consistency of regression estimates based on normalized radial basis function networks when the network parameters are chosen by empirical risk minimization.

Abstract: This paper presents the results of a study aimed at the development of a system for short-term electric power load forecasting. This was attempted by training feedforward neural networks (FFNNs) and cosine radial basis function (RBF) neural networks to predict future power demand based on past power load data and weather conditions. This comparison indicates that both neural network models exhibit comparable performance when tested on the training data but cosine RBF neural networks generalize better since they outperform considerably FFNNs on the testing data.

Abstract: In this paper a special higher order neuron, the hypersphere neuron, is introduced. By embedding Euclidean space in a conformal space, hyperspheres can be expressed as vectors. The scalar product of points and spheres in conformal space, gives a measure for how far a point lies inside or outside a hypersphere. It will be shown that a hypersphere neuron may be implemented as a perceptron with two bias inputs. By using hyperspheres instead of hyperplanes as decision surfaces, a reduction in computational complexity can be achieved for certain types of problems. Furthermore, it will be shown that Multi-Layer Percerptrons (MLP) based on such neurons are similar to Radial Basis Function (RBF) networks. It is also found that such MLPs can give better results than RBF networks of the same complexity. The abilities of the proposed MLPs are demonstrated on some classical data for neural computing, as well as on real data from a particular computer vision problem.