This paper presents numerical solution of elliptic partial differential equations Poisson’s equation using a combination of logarithmic and multiquadric radial basis function networks. This method uses a special combination between logarithmic and multiquadric radial basis functions with a parameter r. Further, the condition number which arises in the process is discussed, and a comparison is m...

With the aim of classifying sperm whales, this report compares two methods that can use Gaussian functions, a radial basis function network, and support vector machines which were trained with two different approaches known as C-SVM and ν-SVM. The methods were tested on data recordings from seven different male sperm whales, six containing single click trains and the seventh containing a comple...

in this paper we investigate a new notion of bases in hilbert spaces and similarto fusion frame theory we introduce fusion bases theory in hilbert spaces. we also introducea new denition of fusion dual sequence associated with a fusion basis and show that theoperators of a fusion dual sequence are continuous projections. next we dene the fusionbiorthogonal sequence, bessel fusion basis, hilbe...

We extend the nearest prototype classifier to a generalized nearest prototype classifier (GNPC). The GNPC uses "soft" labeling of the prototypes in the classes, thereby encompassing a variety of classifiers. Based on how the prototypes are found we distinguish between presupervised and postsupervised GNPC designs. We derive the conditions for optimality (relative to the standard Bayes error rat...

A radial basis function network (RBFN) method is proposed to reconstruct daily Sea surface temperatures (SSTs) with limited SST samples. For the purpose of evaluating the SSTs using this method, non-biased SST samples in the Pacific Ocean (10°N–30°N, 115°E–135°E) are selected when the tropical storm Hagibis arrived in June 2014, and these SST samples are obtained from the OISST products accordi...

A non-linear version of the multivariate statistical technique of canonical correlation analysis (CCA) is proposed through the integration of a radial basis function (RBF) network. The advantage of the RBF network is that the solution of linear CCA can be used to train the network and hence the training effort is minimal. Also the canonical variables can be extracted simultaneously. It is shown...

In this paper, we study the incorporation of the support vector machine (SVM) into the (hierarchical) mixture of experts model to form a support vector mixture. We show that, in both classification and regression problems, the use of a support vector mixture leads to quadratic programming (QP) problems that are very similar to those for a SVM, with no increase in the dimensionality of the QP pr...

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...

Pattern classiication may be viewed as an ill-posed, inverse problem to which the method of regularization be applied. In doing so, a proper theoretical framework is provided for the application of radial basis function (RBF) networks to pattern classiication, with strong links to the classical kernel regression estimator (KRE)-based classiiers that estimate the underlying posterior class densi...

A method of evaluating matrix elements between polynomial basis functions is proposed involving the explicit expansion of the operator in terms of the polynomial. The method is shown to have several advantages over the direct evaluation of these matrix elements by Gaussian quadrature, including savings of up to a factor of 6N for an N-dimensional integral. Application to the calculation of poly...