Abstract: Bankruptcy prediction is one of the major business classification problems. In this paper, we use four different techniques (1) logit model, (2) quadratic interval logit model, (3) backpropagation multi-layer perceptron (i.e., MLP), and (4) radial basis function network (i.e., RBFN) to predict bankrupt and non-bankrupt firms in England. The average hit ratio of four methods range from 91.15% to 77.05%. The original classification accuracy and the validation test results indicate that RBFN outperforms the other models.

Abstract: We propose an algorithm for the global optimization of expensive and noisy black box functions using a surrogate model based on radial basis functions (RBFs). A method for RBF-based approximation is introduced in order to handle noise. New points are selected to minimize the total model uncertainty weighted against the surrogate function value. The algorithm is extended to multiple objective functions by instead weighting against the distance to the surrogate Pareto front; it therefore constitutes the first algorithm for expensive, noisy and multiobjective problems in the literature. Numerical results on analytical test functions show promise in comparison to other (commercial) algorithms, as well as results from a simulation based optimization problem.

Abstract: We consider a multiscale approximation scheme at scattered sites for functions in Sobolev spaces on the unit sphere $\mathbb{S}^n$. The approximation is constructed using a sequence of scaled, compactly supported radial basis functions restricted to $\mathbb{S}^n$. A convergence theorem for the scheme is proved, and the condition number of the linear system is shown to stay bounded by a constant from level to level, thereby establishing for the first time a mathematical theory for multiscale approximation with scaled versions of a single compactly supported radial basis function at scattered data points.

Abstract: Support Vector Machines, a new generation learning system based on recent advances in statistical learning theory deliver state-of-the-art performance in real-world applications such as text categorization, hand-written character recognition, image classification, bio-sequence analysis etc for the classification and regression. This paper emphasizes the classification task with Support Vector Machine. It has several kernel functions including linear, polynomial and radial basis for performing classification. Our comparison between polynomial and radial basis kernel functions for selected feature conclude that radial basis function is preferable than polynomial for large datasets.

Abstract: We present a neuro-fuzzy controller for intelligent cruise control of semiautonomous vehicles. This paper addresses the problem of longitudinal control that aims at regulating the speed of the controlled vehicle in order to maintain constant time headway with respect to the vehicle in front. A fuzzy radial basis function network (FRBFN) longitudinal controller is designed to incorporate the merits of fuzzy logics as well as neural networks. The FRBFN is prestructured, and its parameters are configured such that they are associated with their physical meaning. The parameters of the output layer are learned online via gradient algorithm. An attractive feature of the proposed method is that it does not require the training data and the vehicle longitudinal dynamic model. Simulation results on a vehicle theoretical model are provided to demonstrate the effectiveness of this controller. In order to investigate the proposed control algorithms in real-life situations, a small-scaled vehicle with computer and sensors onboard is developed. Experimental results of a conventional PID controller and the FRBFN controller are provided for comparison.

Abstract: Associative memory networks (AMNs) based on radial basis functions (RBFs) are often used to model complex and nonlinear systems, as they can approximate nonlinear systems with arbitrary accuracy and can be trained from data. However, good generalization results can only be obtained if the structure of the RBF network is suitably chosen. An approach to select the structure of the RBF networks based on the support vectors (SVs) of the support vector machine (SVM) has been proposed. The main advantage of this approach is that the structure of the network can be obtained objectively, as the SVs of the SVM are obtained from a constrained optimization for a given error bound. For convenience, this class of AMNs is referred to as support vector radial basis function networks (SVRBFNs). In this paper, the modelling of the relationship between rainfall and river discharges of the Fuji river using the SVRBFN is presented. As there are large outliers in the modelling errors arising from the data collection process, ...

Abstract: It is well known that single hidden layer feedforward networks with radial basis function (RBF) kernels are universal approximators when all the parameters of the networks are obtained through all kinds of algorithms. However, as observed in most neural network implementations, tuning all the parameters of the network may cause learning complicated, poor generalization, overtraining and unstable. Unlike conventional neural network theories, this brief gives a constructive proof for the fact that a decay RBF neural network with n + 1 hidden neurons can interpolate n + 1 multivariate samples with zero error. Then we prove that the given decay RBFs can uniformly approximate any continuous multivariate functions with arbitrary precision without training. The faster convergence and better generalization performance than conventional RBF algorithm, BP algorithm, extreme learning machine and support vector machines are shown by means of two numerical experiments.

Abstract: The national bridge inventory (NBI) system, a database of visual inspection records that tallies the condition of bridge elements, is used by transportation agencies to manage the rehabilitation of the aging U.S. highway infrastructure. However, further use of the database to forecast degradation, and thus improve maintenance strategies, is limited due to its complexity, nonlinear relationship, unbalanced inspection records, subjectivity, and missing data. In this study, soft computing methods were applied to develop damage prediction models for bridge abutment walls using the NBI database. The methods were multilayer perceptron network, radial basis function network, support vector machine, supervised self-organizing map, fuzzy neural network, and ensembles of neural networks. An ensemble of neural networks with a novel data organization scheme and voting process was the most efficient model, identifying damage with an accuracy of 86%. Bridge deterioration curves were derived using the prediction models and compared with inspection data. The results show that well developed damage prediction models can be an asset for efficient rehabilitation management of existing bridges as well as for the design of new ones.

Abstract: This article presents the implementation of position control of a mobile inverted pendulum (MIP) system by using the radial basis function (RBF) network. The MIP has two wheels to move on the plane and to balance the pendulum. The MIP is a nonlinear system whose dynamics is nonholonomic. The goal of this study was to control the MIP to maintain the balance of the pendulum while tracking a desired position of the cart. The reference compensation technique scheme is used as a neural network control method for the MIP. The back-propagation learning algorithm of the RBF network is derived for online learning and control. The control algorithm has been embedded on a DSP 2812 board to achieve real-time control. Experimental results are conducted and show successful control performances of both balancing and tracking the desired position of the MIP.

Abstract: In this paper a Local Linear Radial Basis Function Neural Network (LLRBFN) is presented. The difference between the proposed neural network and the conventional Radial Basis Function Neural Network (RBFN) is connection weights between the hidden layer and the output layer which are replaced by a local linear model in the LLRBFN. A modified Particle Swarm Optimization (PSO) with hunter particles is introduced for training the LLRBFN. The proposed methods have been applied for prediction of financial time-series and the result shows the feasibility and effectiveness.

Abstract: The weight-decay technique is an effective approach to handle overfitting and weight fault. For fault-free networks, without an appropriate value of decay parameter, the trained network is either overfitted or underfitted. However, many existing results on the selection of decay parameter focus on fault-free networks only. It is well known that the weight-decay method can also suppress the effect of weight fault. For the faulty case, using a test set to select the decay parameter is not practice because there are huge number of possible faulty networks for a trained network. This paper develops two mean prediction error (MPE) formulae for predicting the performance of faulty radial basis function (RBF) networks. Two fault models, multiplicative weight noise and open weight fault, are considered. Our MPE formulae involve the training error and trained weights only. Besides, in our method, we do not need to generate a huge number of faulty networks to measure the test error for the fault situation. The MPE formulae allow us to select appropriate values of decay parameter for faulty networks. Our experiments showed that, although there are small differences between the true test errors (from the test set) and the MPE values, the MPE formulae can accurately locate the appropriate value of the decay parameter for minimizing the true test error of faulty networks.

Abstract: This paper describes an internal combustion engine fault diagnosis system using the manifold pressure of the intake system. The manifold pressure of the engine intake system always demonstrates the engine condition and affects the volumetric efficiency, fuel consumption and performance of internal combustion engines. Manifold pressure is well known to be detrimental to engine system stability and performance and it must be considered during regular maintenance. Conventional engine diagnostic technology using manifold pressure in intake system already exists through analyzing the differences between signals and depends on the experience of the technician. Obviously, the conventional detection is not a precise approach for manifold pressure detection when the engine in operation condition. In the present study, a system consisted of manifold pressure signal feature extraction using discrete wavelet transform (DWT) and fault recognition using the neural network technique is proposed. To verify the effect of the proposed system for identification, both the radial basis function network (RBFN) and generalized regression neural network (GRNN) are used and compared in this study. The experimental results indicated the proposed system using manifold pressure signal as data input is effective for engine fault diagnosis in the experimental engine platform.

Abstract: Polynomial neural networks have been known to exhibit useful properties as classifiers and universal approximators. In this study, we introduce a concept of polynomial-based radial basis function neural networks (P-RBF NNs), present a design methodology and show the use of the networks in classification problems. From the conceptual standpoint, the classifiers of this form can be expressed as a collection of "if-then" rules. The proposed architecture uses two essential development mechanisms. Fuzzy clustering (Fuzzy C-Means, FCM) is aimed at the development of condition parts of the rules while the corresponding conclusions of the rules are formed by some polynomials. A detailed learning algorithm for the P-RBF NNs is developed. The proposed classifier is applied to two-class pattern classification problems. The performance of this classifier is contrasted with the results produced by the "standard" RBF neural networks. In addition, the experimental application covers a comparative analysis including several previous commonly encountered methods such as standard neural networks, SVM, SOM, PCA, LDA, C4.5, and decision trees. The experimental results reveal that the proposed approach comes with a simpler structure of the classifier and better prediction capabilities.

Abstract: In order to efficiently find the optimal design of structures subjected to earthquake loading two strategies are adopted. In the first strategy, a neural system consisting of self organizing map (SOM) and radial basis function (RBF) neural networks is employed to predict the time history responses of structures. The neural system is termed as self organizing radial basis function (SORBF) networks. To train SORBF, the input-output samples are classified by employing SOM clustering, and then an RBF neural network is trained for each cluster by using the data located. In the second strategy, an improved genetic algorithm, the so-called virtual subpopulation (VSP), is employed to find the optimum design. To improve the performance generality of the SORBF, a VSP based optimal approach is employed. Two structures are designed for optimal weight using exact and approximate time history analyses. The numerical results demonstrate the efficiency and computational advantages of the proposed methodology.

Abstract: In this paper, a stable backpropagation algorithm is used to train an online evolving radial basis function neural network. Structure and parameters learning are updated at the same time in our algorithm, we do not make difference in structure learning and parameters learning. It generates groups with an online clustering. The center is updated to achieve the center is near to the incoming data in each iteration, so the algorithm does not need to generate a new neuron in each iteration, i.e., the algorithm does not generate many neurons and it does not need to prune the neurons. We give a time varying learning rate for backpropagation training in the parameters. We prove the stability of the proposed algorithm.

Abstract: In this paper, a groundwater level forecasting model is proposed by combining the theory of self-organizing map (SOM) and radial basis function network (RBFN). The proposed model is referred to as SOM-RBFN model. Recently, RBFN has been applied in time series forecasting. Traditionally, the number of hidden units and the positioning of the radial basis centers are crucial problems for establishing RBFN. The proposed model can decide the number of RBFN’s hidden units with using the two-dimensional feature map which is constructed by SOM, and then it can determine the positioning of the radial basis centers easily. The proposed model is applied to actual groundwater level data in southern Taiwan from 1997 to 2003. It is found that the multisite model can predict the 1 month ahead groundwater level more precisely than the single-site model. Moreover, it is also found that the four-site model is more competent in predicting groundwater level as compared to the single-site model and six-site model. Therefore, ...

Abstract: In this paper we address the problem of optimal centre placement for scattered data approximation using radial basis functions (RBFs) by introducing the concept of floating centres. Given an initial least-squares solution, we optimize the positions and the weights of the RBF centres by minimizing a non-linear error function. By optimizing the centre positions, we obtain better approximations with a lower number of centres, which improves the numerical stability of the fitting procedure. We combine the non-linear RBF fitting with a hierarchical domain decomposition technique. This provides a powerful tool for surface reconstruction from oriented point samples. By directly incorporating point normal vectors into the optimization process, we avoid the use of off-surface points which results in less computational overhead and reduces undesired surface artefacts. We demonstrate that the proposed surface reconstruction technique is as robust as recent methods, which compute the indicator function of the solid described by the point samples. In contrast to indicator function based methods, our method computes a global distance field that can directly be used for shape registration.

Abstract: Breast cancer is the second leading cause of cancer deaths in women worldwide and occurs in nearly one out of eight women Currently there are three techniques to diagnose breast cancer: mammography, FNA (Fine Needle Aspirate) and surgical biopsy In this paper we develop an integrated expert system for diagnosis, prognosis and prediction for breast cancer using soft computing techniques The basic aim is to compare the various neural network models from the recent literature Breast cancer database used for this purpose is from the University of Wisconsin (UCI) Machine Learning Repository Three different data sets have been used, each employing different diagnostic technique It can use diagnosis, prognosis and survivability prediction of breast cancer patient in one intelligent system We implement six models of neural networks namely Back Propagation Algorithm, Radial Basis Function Networks, Learning vector Quantization, Probabilistic Neural Networks, Recurrent Neural Network, and Competitive Neural network Experimental Results show that different models give optimal performance for different types of data sets However, all the models are able to solve the problem to a reasonable extent