Abstract: A new class of data structures called "bumptrees" is described. These structures are useful for efficiently implementing a number of neural network related operations. An empirical comparison with radial basis functions is presented on a robot arm mapping learning task. Applications to density estimation, classification, and constraint representation and learning are also outlined.

Abstract: We have created a radial basis function network that allocates a new computational unit whenever an unusual pattern is presented to the network. The network learns by allocating new units and adjusting the parameters of existing units. If the network performs poorly on a presented pattern, then a new unit is allocated which memorizes the response to the presented pattern. If the network performs well on a presented pattern, then the network parameters are updated using standard LMS gradient descent. For predicting the Mackey Glass chaotic time series, our network learns much faster than do those using back-propagation and uses a comparable number of synapses.

Abstract: The radial basis function algorithm is used to classify impulse radar waveforms from asphalt-covered bridge decks. A brief description of the impulse radar scenario is given, and the radial basis function algorithm is summarized. The classification results obtained using the algorithm are presented. Excellent success was obtained, with classification accuracies up to 99%. Training the radial basis function classifier is faster and less complex than training a back-propagation-based network, since the simple least-mean-squares (LMS) algorithm can be used to obtain estimates of the optimum weight values

Abstract: We examine the ability of radial basis functions (RBFs) to generalize. We compare the performance of several types of RBFs. We use the inverse dynamics of an idealized two-joint arm as a test case. We find that without a proper choice of a norm for the inputs, RBFs have poor generalization properties. A simple global scaling of the input variables greatly improves performance. We suggest some efficient methods to approximate this distance metric.

Abstract: Many neural networks are constructed to learn an input-output mapping from examples. This problem is related to classical approximation techniques including regularization theory. Regularization is equivalent to a class of threelayer networks which we call regularization networks or Hyper Basis Functions. The strong theoretical foundation of regularization networks provides us with a better understanding of why they work and how to best choose a specific network and parameters for a given problem. Classical regularization theory can be extended in order to improve the quality of learning performed by Hyper Basis Functions. For example the centers of the basis functions and the norm weights can be optimized. Many Radial Basis Functions often used for function interpolation are provably Hyper Basis Functions. 1.© (1990) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Abstract: We develop a sequential adaptation algorithm for radial basis function (RBF) neural networks of Gaussian nodes, based on the method of successive F-Projections. This method makes use of each observation efficiently in that the network mapping function so obtained is consistent with that information and is also optimal in the least L2-norm sense. The RBF network with the F-Projections adaptation algorithm was used for predicting a chaotic time-series. We compare its performance to an adaptation scheme based on the method of stochastic approximation, and show that the F-Projections algorithm converges to the underlying model much faster.

Abstract: Nonlinear signal processing using radial basis functions1. J. Shepherd and D. S. BroomheadRoyal Signals and Radar Establishment, St. Andrew's Road,Malvern, Worcestershire, WR14 3P5, UKABSTRACTA procedure for multidimensional nonlinear modelling and interpolation is described which employs themethod of radial basis function analysis. A systolic array for efficiently performing the associated computation forboth the modelling and interpolation modes recursively in time is also described. Conditions are given for the furtherimprovement of efficiency in the algorithm when the input data constitute a time series, and an associated processingstructure is outlined.1. INTRODUCTION

Abstract: : This report summarizes research efforts on (1) the demonstration of holographic degeneracies in associative memories, (2) the procedure for designing fractal grids for planar holograms, (3) the experimental demonstration of one and two layer neural networks that are designed with such fractal sampling grids, (4) the experimental demonstration of dynamic holographic memories that are capable of an arbitrarily long sequence of adaptations, (5) the optical implementation of the Kanerva's network for hand-written character recognition, (6) the development of an anti-Hebbian local learning algorithm for training multi-layer neural networks, (7) the experimental demonstration of optical radial basis function network, and (8) the demonstration of a two-layer local-representation optical network for real-time face recognition.

Abstract: A radial basis functions neural network is trained to approximate speech spectrograms. We show that such approximations can be useful as a method of extracting known discriminatory features in speech patterns, using CV transition examples. We also argue that such an approximation to a joint time frequency representation can be seen as a description, of the dynamics of speech patterns, that does not make uniform segmentation across different frequency bands.

Abstract: Neural networks are examined in the context of function approximation and the related field of time series prediction. A natural extension of radial basis nets is introduced. It is found that use of an adaptable gradient and normalized basis functions can significantly reduce the amount of data necessary to train the net while maintaining the speed advantage of a net that is linear in the weights. The local nature of the network permits the use of simple learning algorithms with short memories of earlier training data. In particular, it is shown that a one-dimensional Newton method is quite fast and reasonably accurate

Abstract: This paper investigates the identification of discrete-time non-linear systems using radial basis functions. A forward regression algorithm based on an orthogonal decomposition of the regression matrix is employed to select a suitable set of radial basis function centers from a large number of possible candidates and this provides, for the first time, fully automatic selection procedure for identifying parsimonious radial basis function models of structure-unknown non-linear systems. The relationship between neural networks and radial basis functions is discussed and the application of the algorithms to real data is included to demonstrate the effectiveness of this approach.