It is often observed that interpolation based on translates of radial basis functions or non-radial kernels is numerically unstable due to exceedingly large condition of the kernel matrix. But if stability is assessed in function space without considering special bases, this paper proves that kernel–based interpolation is stable. Provided that the data are not too wildly scattered, the L2 or L∞...

One popular class of unsupervised algorithms are competitive algorithms. In the traditional view of competition, only one competitor, the winner, adapts for any given case. I propose to view competitive adaptation as attempting to fit a blend of simple probability generators (such as gaussians) to a set of data-points. The maximum likelihood fit of a model of this type suggests a "softer" form ...

It’s well-known that there is a so-called high-level error bound for multiquadric and inverse multiquadric interpolations, which was put forward by Madych and Nelson in 1992. It’s of the form |f(x)− s(x)| ≤ λ 1 d ‖f‖h where 0 < λ < 1 is a constant, d is the fill distance which roughly speaking measures the spacing of the data points, s(x) is the interpolating function of f(x), and h denotes the...

We present a new scheme to robustly detect a type of human attentive behavior, which we call frequent change in focus of attention (FCFA), from video sequences. FCFA behavior can be easily perceived by people as temporal changes of human head pose (normally the pan angle). For recognition of this behavior by computer, we propose an algorithm to estimate the head pan angle in each frame of the s...

In this paper the authors derive a higher-order shear deformation theory for modelling functionally graded plates accounting for extensibility in the thickness direction. The explicit governing equations and boundary conditions are obtained using the principle of virtual displacements under Carrera’s Unified Formulation and then interpolated by collocation with radial basis functions. The effic...

Abstract. We construct a new adaptive algorithm for radial basis functions (RBFs) method applied to interpolation, boundary-value, and initialboundary-value problems with localized features. Nodes can be added and removed based on residuals evaluated at a finer point set. We also adapt the shape parameters of RBFs based on the node spacings to prevent the growth of the conditioning of the inter...

A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible (1) objective comparisons between solutions using alternative network architectures, (2) objective stopping rules for network pruning or growing procedures, (3) objective choice of magnitude and type of weight decay terms or additive regularizers (for penal...

The standard error bounds for interpolation by kernels or radial basis functions are generalized to symmetric PDE collocation problems. This involves generalized Power Functions, and these can be explicitly calculated. Final error bounds then are a product of Power Function values and the norm of the solution in the native space of the kernel. Since the latter can also be estimated well, the wh...

It’s well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992. It’s of the form|f(x)− s(x)| ≤ (Cd) c d ‖f‖h where C, c are constants, h is the Gaussian function, s is the interpolating function, and d is called fill distance which, roughly speaking, measures the spacing of the points at which interpolation occurs. This error bound gets small ve...

Generic imaging models can be used to represent any camera. Current generic models are discrete and define a mapping between each pixel in the image and a straight line in 3D space. This paper presents a modification of the generic camera model that allows the simplification of the calibration procedure. The only requirement is that the coordinates of the 3D projecting lines are related by func...