The problem is said to be tractable if there exist constants c, α, β independent of q (but possibly dependent on μ and F) such that En(F , μ) ≤ cqαn−β. We explore different regions (including manifolds), function classes, and measures for which this problem is tractable. Our results include tractability theorems for integration with respect to non-tensor product measures, and over unbounded and...

Two difficulties are involved with traditional RBF networks: the initial configuration of an RBF network needs to be determined by a trial-and-error method, and the performance suffers degradation when the desired locations of the center of the RBF are not suitable. A novel RBF network is proposed to overcome these difficulties. A new radial basis function is used for hidden nodes, and the numb...

Despite such very appealing features of the radial basis function (RBF) as inherent meshfree and independent of dimension and geometry, the various RBF-based schemes [1] of solving partial differential equations (PDE’s) still confront some deficiencies. For instances, the lack of easy-to-use spectral convergent RBFs, ill-conditioning and costly evaluation of full interpolation matrix. The purpo...

In this paper, a new approach for the compensation of unknown periodic disturbances by means of a neural network is presented. The neural controller supports the conventional controller by suppressing periodic disturbances. This is done by online learning in order to adapt to different operating conditions and to time varying unknown disturbances. The neural network learns an optimal compensati...

The paper describes the use of radial basis function neural networks with Gaussian basis functions to classify incomplete feature vectors. The method exploits the fact that any marginal distribution of a defined Gaussian joint distribution can be determined from the mean vector and covariance matrix of the joint distribution. The method is discussed in the context of complete and incomplete tra...

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Radial basis function neural networks (RBFNNs), which is a relatively new class of neural networks, have been investigated for their applicability for prediction of performance and emission characteristics of a diesel engine fuelled with waste cooking oil (WCO). The RBF network...

The behavior of Radial Basis Function (RBF) Networks greatly depends on how the center points of the basis functions are selected. In this work we investigate the use of instance reduction techniques, originally developed to reduce the storage requirements of instance based learners, for this purpose. Five Instance-Based Reduction Techniques were used to determine the set of center points, and ...

In this paper, a supervised technique for training radial basis function (RBF) neural network classifiers is proposed. Such a technique, unlike traditional ones, considers the class memberships of training samples to select the centers and widths of the kernel functions associated with the hidden neurons of an RBF network. The result is twofold: a significant reduction in the overall classifica...

A radial basis function (RBF) neural network approach with a fusion of multiple signal candidates in precision motion control is studied in this paper. Sensor weightages are assigned to sensor measurements according to the selector attributes and are approximated using RBF neural network in multi-sensor fusion. A specific application towards precision motion control of a linear motor system usi...

We propose a self-organising hierarchical Radial Basis Function (RBF) network for functional modelling of large amounts of scattered unstructured point data. The network employs an error-driven active learning algorithm and a multi-layer architecture, allowing progressive bottom-up reinforcement of local features in subdivisions of error clusters. For each RBF subnet, neurons can be inserted, r...