Mean-tracking clustering algorithm for radial basis function centre selection

Radial basis functions can be combined into a network structure that has several advantages over conventional neural network solutions. However, to operate effectively the number and positions of the basis function centres must be carefully selected. Although no rigorous algorithm exists for this purpose, several heuristic methods have been suggested. In this paper a new method is proposed in which radial basis function centres are selected by the mean-tracking clustering algorithm. The mean-tracking algorithm is compared with k means clustering and it is shown that it achieves significantly better results in terms of radial basis function performance. As well as being computationally simpler, the mean-tracking algorithm in general selects better centre positions, thus providing the radial basis functions with better modelling accuracy

Robust initialisation of Gaussian radial basis function networks using partitioned k-means clustering

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.

Dual-orthogonal radial basis function networks for nonlinear time series prediction

A new structure of Radial Basis Function (RBF) neural network called the Dual-orthogonal RBF Network (DRBF) is introduced for nonlinear time series prediction. The hidden nodes of a conventional RBF network compare the Euclidean distance between the network input vector and the centres, and the node responses are radially symmetrical. But in time series prediction where the system input vectors are lagged system outputs, which are usually highly correlated, the Euclidean distance measure may not be appropriate. The DRBF network modifies the distance metric by introducing a classification function which is based on the estimation data set. Training the DRBF networks consists of two stages. Learning the classification related basis functions and the important input nodes, followed by selecting the regressors and learning the weights of the hidden nodes. In both cases, a forward Orthogonal Least Squares (OLS) selection procedure is applied, initially to select the important input nodes and then to select the important centres. Simulation results of single-step and multi-step ahead predictions over a test data set are included to demonstrate the effectiveness of the new approach.

A Learning Function for Parameter Reduction in Spiking Neural Networks with Radial Basis Function

Spiking neural networks - networks that encode information in the timing of spikes - are arising as a new approach in the artificial neural networks paradigm, emergent from cognitive science. One of these new models is the pulsed neural network with radial basis function, a network able to store information in the axonal propagation delay of neurons. Learning algorithms have been proposed to this model looking for mapping input pulses into output pulses. Recently, a new method was proposed to encode constant data into a temporal sequence of spikes, stimulating deeper studies in order to establish abilities and frontiers of this new approach. However, a well known problem of this kind of network is the high number of free parameters - more that 15 - to be properly configured or tuned in order to allow network convergence. This work presents for the first time a new learning function for this network training that allow the automatic configuration of one of the key network parameters: the synaptic weight decreasing factor.

A Learning Function for Parameter Reduction in Spiking Neural Networks with Radial Basis Function

Spiking neural networks - networks that encode information in the timing of spikes - are arising as a new approach in the artificial neural networks paradigm, emergent from cognitive science. One of these new models is the pulsed neural network with radial basis function, a network able to store information in the axonal propagation delay of neurons. Learning algorithms have been proposed to this model looking for mapping input pulses into output pulses. Recently, a new method was proposed to encode constant data into a temporal sequence of spikes, stimulating deeper studies in order to establish abilities and frontiers of this new approach. However, a well known problem of this kind of network is the high number of free parameters - more that 15 - to be properly configured or tuned in order to allow network convergence. This work presents for the first time a new learning function for this network training that allow the automatic configuration of one of the key network parameters: the synaptic weight decreasing factor.

Remaining useful life prediction using elliptical basis function network and Markov Chain

This paper presents a novel method for remaining useful life prediction using the Elliptical Basis Function (EBF) network and a Markov chain. The EBF structure is trained by a modified Expectation-Maximization (EM) algorithm in order to take into account the missing covariate set. No explicit extrapolation is needed for internal covariates while a Markov chain is constructed to represent the evolution of external covariates in the study. The estimated external and the unknown internal covariates constitute an incomplete covariate set which are then used and analyzed by the EBF network to provide survival information of the asset. It is shown in the case study that the method slightly underestimates the remaining useful life of an asset which is a desirable result for early maintenance decision and resource planning.

A Radial Basis Function Approach to Financial Time Series Analysis

Nonlinear multivariate statistical techniques on fast computers offer the potential to capture more of the dynamics of the high dimensional, noisy systems underlying financial markets than traditional models, while making fewer restrictive assumptions. This thesis presents a collection of practical techniques to address important estimation and confidence issues for Radial Basis Function networks arising from such a data driven approach, including efficient methods for parameter estimation and pruning, a pointwise prediction error estimator, and a methodology for controlling the "data mining'' problem. Novel applications in the finance area are described, including customized, adaptive option pricing and stock price prediction.

Automated cross-modal mapping in robotic eye/hand systems using plastic radial basis function networks

Q. Meng and M. H Lee, Automated cross-modal mapping in robotic eye/hand systems using plastic radial basis function networks, Connection Science, 19(1), pp 25-52, 2007.

Error-driven active learning in growing radial basis function networks for early robot learning

Q. Meng and M.H. Lee, 'Error-driven active learning in growing radial basis function networks for early robot learning', 2006 IEEE International Conference on Robotics and Automation (IEEE ICRA 2006), 2984-90, Orlando, Florida, USA.

Two-stage mixed discrete-continuous identification of radial basis function (RBF) neural models for nonlinear systems

The identification of nonlinear dynamic systems using radial basis function (RBF) neural models is studied in this paper. Given a model selection criterion, the main objective is to effectively and efficiently build a parsimonious compact neural model that generalizes well over unseen data. This is achieved by simultaneous model structure selection and optimization of the parameters over the continuous parameter space. It is a mixed-integer hard problem, and a unified analytic framework is proposed to enable an effective and efficient two-stage mixed discrete-continuous; identification procedure. This novel framework combines the advantages of an iterative discrete two-stage subset selection technique for model structure determination and the calculus-based continuous optimization of the model parameters. Computational complexity analysis and simulation studies confirm the efficacy of the proposed algorithm.