Abstract: In recent years neural computing has emerged as a practical technology, with successful applications in many fields. The majority of these applications are concerned with problems in pattern recognition, and make use of feedforward network architectures such as the multilayer perceptron and the radial basis function network. Also, it has become widely acknowledged that successful applications of neural computing require a principled, rather than ad hoc, approach. (From the preface to "Neural Networks for Pattern Recognition" by C.M. Bishop, Oxford Univ Press 1995.) This NATO volume, based on a 1997 workshop, presents a coordinated series of tutorial articles covering recent developments in the field of neural computing. It is ideally suited to graduate students and researchers.

Abstract: We apply the method of complexity regularization to derive estimation bounds for nonlinear function estimation using a single hidden layer radial basis function network. Our approach differs from previous complexity regularization neural-network function learning schemes in that we operate with random covering numbers and l/sub 1/ metric entropy, making it possible to consider much broader families of activation functions, namely functions of bounded variation. Some constraints previously imposed on the network parameters are also eliminated this way. The network is trained by means of complexity regularization involving empirical risk minimization. Bounds on the expected risk in terms of the sample size are obtained for a large class of loss functions. Rates of convergence to the optimal loss are also derived.

Abstract: In radial basis function networks, placement of centers has been one of the problems addressed and has 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. Supervised learning of centers seem to offset the advantages achieved by the two stage learning of the 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 centers. This can be done by evaluating whether moving the centers would decrease the error. In this paper we have calculated bounds for the gradient and Hessian of the error considered as a function of centers for networks of fixed size. Using these bounds it is possible to know by how much one can reduce the error by changing the centers. Furthermore, step size can be specified to achieve a guaranteed amount of reduction in error.

Abstract: The back-propagation neural network (BPN) model has been the most popular form of artificial neural network model used for forecasting, particularly in economics and finance. It is a static (feed-forward) model which has a learning process in both hidden and output layers. In this paper, we compare the performance of the BPN model with that of two other neural network models, i.e., radial basis function network (RBFN) model and recurrent neural network (RNN) model, in the context of forecasting inflation. The RBFN model is a hybrid model whose learning process is much faster than the BPN model and able to generate almost the same results as the BPN model. The RNN model is a dynamic model which allows feedback from other layers to input layer, enabling it to capture the dynamic behavior of the series. The results of the ANN models are also compared with those of the econometric time series models.

Abstract: Presents a neural network called the normalized radial basis function (NRBF) neural network. The NRBF integrates techniques from two similar neural networks: the general regression neural network (GRNN) and the radial basis function (RBF) neural network. The NRBF is identical to the standard radial basis function (RBF) network except the hidden layer outputs are normalized before being passed through the output layer. The normalization of the hidden layer weights is shown to improve the extrapolation performance of the conventional RBF network. We have reason to believe that under normal circumstances the NRBF outperforms the RBF and the GRNN.

Abstract: Radial basis functions for discrimination and regression have been used with some success in a wide variety of applications. Here, we investigate the optimal choice for the form of the basis functions and present an iterative strategy for obtaining the function in a regression context using a conjugate gradient-based algorithm together with a nonparametric smoother. This is developed in a discrimination framework using the concept of optimal scaling. Results are presented for a range of simulated and real data sets.

Abstract: An unsupervised neural based approach to financial forecasting is presented; its performance is compared with that from a statistical technique and two other standard neural network techniques. The authors show that the unsupervised network outperforms multilayer perceptrons, radial basis function network and a standard ARIMA model.

Abstract: Consider a multilayer perceptron (MLP) with d inputs, a single hidden sigmoidal layer and a linear output. By adding an additional d inputs to the network with values set to the square of the first d inputs, properties reminiscent of higher-order neural networks and radial basis function networks (RBFN) are added to the architecture with little added expense in terms of weight requirements. Of particular interest, this architecture has the ability to form localized features in a d-dimensional space with a single hidden node but can also span large volumes of the input space; thus, the architecture has the localized properties of an RBFN but does not suffer as badly from the curse of dimensionality. I refer to a network of this type as a SQuare Unit Augmented, Radially Extended, MultiLayer Perceptron (SQUARE-MLP or SMLP).

Abstract: One of the main problems associated with artificial neural networks on-line learning methods is the estimation of model order. In this paper, we report about a new approach to constructing a resource-allocating radial basis function network exploiting weights adaptation using recursive least-squares technique based on Givens QR decomposition. Further, we study the performance of pruning strategy we introduced to obtain the same prediction accuracy of the network with lower model order. The proposed methods were tested on the task of Mackey-Glass time-series prediction. Order of resulting networks and their prediction performance were superior to those previously reported by Platt [12].

Abstract: A genetic algorithm and recursive least squares (RLS) learning algorithm for a Gaussian radial basis function network is described, for modelling and predicting nonlinear time series. Better generalisation performance can be achieved than that of the usual clustering and RLS method.

Abstract: This paper presents a Mahalanobis based radial basis function network (RBF) receiver structure with reduced complexity. It is also illustrated, how the RBF receiver could be employed as a multiuser detector. The RBF structure has superior performance over linear receiver structures and is equivalent to MLSD in an AWGN channel. However, a drawback is its complexity in multipath channels. Ideas from pattern recognition are exploited to reduce its complexity for multipath scenarios with little performance loss.

Abstract: In the present paper, Wavelet Networks, are proven to be, as well as many other neural paradigms, a speci c case of the generic paradigm named Weighted Radial Basis Functions Networks. Moreover, a fair comparison between Wavelet and more traditional WRBF networks for function approximation is attempted, in order to demonstrate that the performance depends only on how good the chosen mother/activation function \ ts" the function itself.

Abstract: This paper proposes supervised learning algorithms based on gradient descent for training reformulated radial basis function (RBF) neural networks. Such RBF models employ radial basis functions whose form is determined by admissible generator functions. RBF networks with Gaussian radial basis functions are generated by exponential generator functions. A sensitivity analysis provides the basis for selecting generator functions by investigating the effect of linear, exponential and logarithmic generator functions on gradient descent learning. Experiments involving reformulated RBF networks indicate that the proposed gradient descent algorithms guarantee fast learning and very satisfactory function approximation capability.

Abstract: The standard risk-sensitive (or exponential quadratic) functional used for robust control and filtering for linear systems is generalized. It is then shown that under relatively mild conditions, a function can be approximated, to any desired degree of accuracy with respect to these general risk-sensitive functionals, by a multilayer perceptron or a radial basis function network.

Abstract: This paper develops the concept of usefulness in the context of supervised learning. We argue that usefulness can be used to improve the performance of classification rules (as measured by error rate), as well to reduce their storage (or their derivation). We also indicate how usefulness can be applied in a dynamic setting, in which the distribution of at least one class is changing with time. Three algorithms are used to exemplify our proposals. We first review a dynamic nearest neighbour classifier, and then develop dynamic versions of Learning Vector Quantization and a Radial Basis Function network. All the algorithms are adapted to capture dynamic aspects of real-world data sets by keeping a record of usefulness as well as considering the age of the observations. These methods are tried out on real data from the credit industry.1

Abstract: The use of a self-organising neural network as a feedforward compensator for robot tracking control applications is proposed. The topology of the input space is adaptively mapped onto a set of neurons where each neuron represents a discrete cell in the input domain. Within each cell, a linear mapping is established between the input and output space. The training of such a network involves training of a weight vector that represents the topology of the input space and weight vectors (action space weights) that linearly code an input pattern to action space. In the first phase of network training, a ‘neural-gas’ algorithm is employed for learning the topology of the input space while weight vectors representing control action space is learned by backpropagating feedback control action. During this phase of learning, the weights associated with neurons in the neighbourhood of winning neurons are also updated. In the second stage, a recursive least squares based estimation scheme is applied to fine tune the action space weights associated with winning neurons only, without disturbing the input topology map learned in the first phase. The proposed scheme has been compared with multilayered network (MLN) and radial basis function network (RBFN) based inverse dynamics learning schemes. Simulation results show that the proposed scheme has better generalisation capability than both MLN and RBFN.

Abstract: In this paper, we present a real-time dynamic gesture recognition system utilizing radial basis function network techniques and dynamic time warping method. The goal is to design a space invariant and time interval invariant system which can distinguish between various spatio-temporal data representing hand gestures. The prototype and user interface have been realized. The resulting system possesses characteristics of real-time and online learning, user-defined gestures and functionality, and high recognition rate. We demonstrate a virtual reality application in which the object is manipulated by the proposed gesture recognition method.

Abstract: We show in this paper how Neural Networks can be used for Human Face Processing. In Part I, we show how Neural Networks can be viewed as a particular class of Statistical models. We introduce learning as an estimation problem 1, then describe Multi-Layer Perceptrons and Radial Basis Function networks 2, widely used Neural Networks which we will use in Part II, for face processing. We further present Vapnik’s framework for learning 3, show the capacity/generalization dilemma and discuss its implications for Neural Network training and model selection. Vapnik’s ideas lead to a new interesting class of classifier, Support Vector Machines, presented in section 3.2. We then discuss the combination of models 4 and give a formalism which allows to cooperatively train multi-modular Neural Networks architectures. Finally, we present a multi-modular architecture to perform “Segmentation-Recognition in the loop” 5.