We provide a new way to compute and evaluate Gaussian radial basis function interpolants in a stable way with a special focus on small values of the shape parameter, i.e., for “flat” kernels. This work is motivated by the fundamental ideas proposed earlier by Bengt Fornberg and his co-workers. However, following Mercer’s theorem, an L2(R, ρ)-orthonormal expansion of the Gaussian kernel allows u...

We present an approximation scheme for support vector machine models that use an RBF kernel. A second-order Maclaurin series approximation is used for exponentials of inner products between support vectors and test instances. The approximation is applicable to all kernel methods featuring sums of kernel evaluations and makes no assumptions regarding data normalization. The prediction speed of a...

We determine the asymptotic limit of the function computed by support vector machines (SVM) and related algorithms that minimize a regularized empirical convex loss function in the reproducing kernel Hilbert space of the Gaussian RBF kernel, in the situation where the number of examples tends to infinity, the bandwidth of the Gaussian kernel tends to 0, and the regularization parameter is held ...

When large datasets are aggregated into smaller data sizes we need more complex data tables e.g. interval type instead of standard ones. Our investigation in this paper aims at extending kernel methods to interval data analysis and using graphical methods to explain the obtained results. No algorithmic changes are required from the usual case of continuous data other than the modification of th...

We describe a Fourier Volume Rendering (FVR) algorithm for datasets that are irregularly sampled and require anisotropic (e.g., elliptical) kernels for reconstruction. We sample the continuous frequency spectrum of such datasets by computing the continuous Fourier transform of the spatial interpolation kernel which is a radially symmetric Gaussian basis function (RBF) that may be anisotropicall...

This contribution proposes a novel probability density function (PDF) estimation based over-sampling (PDFOS) approach for two-class imbalanced classification problems. The classical Parzen-window kernel function is adopted to estimate the PDF of the positive class. Then according to the estimated PDF, synthetic instances are generated as the additional training data. The essential concept is to...

This Research presents the effects of interaction between various Kernel functions and different Feature Selection Techniques for improving the learning capability of Support Vector Machine (SVM) in detecting email spams. The interaction of four Kernel functions of SVM i. e. "Normalised Polynomial Kernel (NP)", "Polynomial Kernel (PK)", "Radial Basis Function Kernel (RB...

This paper presents a simple estimate to determine the width of Gaussian kernel with the adaptive scaling technique. The Gaussian kernel is widely employed in Radial Basis Function (RBF) network, Support Vector Machine (SVM), Least Squares Support Vector Machine (LS-SVM), Kriging, and so on. It is widely known that the width of the Gaussian kernel in these machine learning techniques plays an i...

In this paper, a meshless method for solving the eigenproblems of plate vibration using the radial basis function (RBF) is proposed. By employing the RBF in the imaginary-part fundamental solution, spurious eigenequations in conjunction with the true ones are obtained at the same time. Mathematical analysis for the appearance of spurious eigenequations by using degenerate kernel and circulant i...

In this paper, a meshless method for the acoustic eigenfrequencies using radial basis function (RBF) is proposed. The coefficients of influence matrices are easily determined by the two-point functions. In determining the diagonal elements of the influence matrices, two techniques, limiting approach and invariant method, are employed. Based on the RBF in the imaginary-part kernel, the method re...