Let (xn) ⊂ R d be a uniformly separated sequence which forms a Fourier frame for PWB2 , the space of square-integrable functions on R d whose Fourier transforms vanish outside the Euclidean unit ball B2. Given λ > 0 and f ∈ PWB2 , there is a unique sequence (aj) in l2 such that the function Iλ(f)(x) := X aje −λ‖x−xj‖ 2 2 , x∈R d , is continuous and square integrable on R, and satisfies the inte...

1 Implementing Radial Basis Functions Using Bump-Resistor Networks John G. Harris University of Florida EE Dept., 436 CSE Bldg 42 Gainesville, FL 32611 [email protected] .edu Abstract| Radial Basis Function (RBF) networks provide a powerful learning architecture for neural networks [6]. We have implemented a RBF network in analog VLSI using the concept of bump-resistors. A bump-resistor is a ...

An elliptical basis function (EBF) network is proposed in this study for the classification of remotely sensed images. Though similar in structure, the EBF network differs from the well-known radial basis function (RBF) network by incorporating full covariance matrices and uses the expectation-maximization (EM) algorithm to estimate the basis functions. Since remotely sensed data often take on ...

ix Resumé xi Remerciements xiii Abbréviations xv I General Introduction 1 0.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0.2 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 0.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 0.4 Outline . . . . . . . . . . . . . . . . . . . . ...

In many cases, multivariate interpolation by smooth radial basis functions converges towards polynomial interpolants, when the basis functions are scaled to become “wide”. In particular, examples show that interpolation by scaled Gaussians seems to converge towards the de Boor/Ron “least” polynomial interpolant. The paper starts by providing sufficient criteria for the convergence of radial int...

We propose a new method for constructing hyperkenels and define two promising special cases that can be computed in closed form. These we call the Gaussian and Wishart hyperkernels. The former is especially attractive in that it has an interpretable regularization scheme reminiscent of that of the Gaussian RBF kernel. We discuss how kernel learning can be used not just for improving the perform...

The Hermite Radial Basis Functions (HRBF) Implicits reconstruct an implicit function which interpolates or approximates scattered multivariate Hermite data (i.e., unstructured points and their corresponding normals). Experiments suggest that HRBF Implicits allow the reconstruction of surfaces rich in details and behave better than previous related methods under coarse and/or nonuniform sampling...