This paper represents a novel algorithm to represent and recognize two dimensional curve based on its convex hull and the Least-Squared modeling. It combines the advantages of the property of the convex hulls that are particularly suitable for affine matching as they are affine invariant and the geometric properties of a contour that make it more or less identifiable. The description scheme and...

We describe an algorithm for complex discrete least squares approximation, which turns out to be very efficient when function values are prescribed in points on the real axis or on the unit circle. In the case of polynomial approximation, this reduces to algorithms proposed by Rutishauser, Gragg, Harrod, Reichel, Ammar and others. The underlying reason for efficiency is the existence of a recur...

In this note, we develop fast and deterministic dimensionality reduction techniques for a family of subspace approximation problems. Let P ⊂ R be a given set of M points. The techniques developed herein find an O(n logM)-dimensional subspace that is guaranteed to always contain a near-best fit n-dimensional hyperplane H for P with respect to the cumulative projection error (∑ x∈P ‖x−ΠHx‖ p 2 )1...

The radial basis function interpolant is known to be the best approximation to a set of scattered data when the error is measured in the native space norm. The approximate moving least squares method, on the other hand, was recently proposed as an efficient approximation method that avoids the solution of the system of linear equations associated with the radial basis function interpolant. In t...

We propose a method of least squares approximation (LSA) for unified yet simple LASSO estimation. Our general theoretical framework includes ordinary least squares, generalized linear models, quantile regression, and many others as special cases. Specifically, LSA can transfer many different types of LASSO objective functions into their asymptotically equivalent least-squares problems. Thereaft...

We study the problem of linear approximation of a signal using the parametric Gamma bases in L2 space. These bases have a time scale parameter which has the effect of modifying the relative angle between the signal and the projection space, thereby yielding an extra degree of freedom in the approximation. Gamma bases have a simple analog implementation which is a cascade of identical lowpass fi...

We study uniform approximation of differentiable or analytic functions of one or several variables on a compact set K by a sequence of discrete least squares polynomials. In particular, if K satisfies a Markov inequality and we use point evaluations on standard discretization grids with the number of points growing polynomially in the degree, these polynomials provide nearly optimal approximant...

We describe a new method for surface reconstruction based on unorganized point clouds without normals. We also present a new algorithm for refining the inital triangulation. The output of the method is a refined triangular mesh with points on the moving least squares surface of the original point cloud.

We introduce moving least squares approximation as an approximation scheme on the sphere. We prove error estimates and approximation orders. Finally, we show certain numerical results. x1. Introduction Recently, approximation on the sphere has become important because of its obvious applications to Meteorology, Oceanography and Geoscience and Geo-engineering in general. Over the last years seve...

Adaptive equalizers are used in digital communication system receivers to mitigate the effects of non-ideal channel characteristics and to obtain reliable data transmission. In this paper, we adopt least squares support vector machines (LS-SVM) for adaptive communication channel equalization. The LS-SVM involves equality instead of inequality constraints and works with a least squares cost func...