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We consider the problem of learning multi-ridge functions of the form f (x) = g(Ax) from point evaluations of f. We assume that the function f is defined on an l(2)-ball in R-d, g is twice continuously differentiable almost everywhere, and A is an element ...
This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities - which are mainly related either to nonlin ...
We present a method for the unsupervised segmentation of textured images using Potts functionals, which are a piecewise-constant variant of the Mumford and Shah functionals. We propose a minimization strategy based on the alternating direction method of mu ...
Scarce work has been done in the analysis of the composition of conserved non-coding elements (CNEs) that are identified by comparisons of two or more genomes and are found to exist in all metazoan genomes. Here we present the analysis of CNEs with a metho ...
We propose a method for accurate and fast reconstruction of the interior of a 2D or 3D tomographic image from its incomplete local Radon transform. Unlike the existing interior tomography work with 2D total variation, the proposed algorithm guarantees exac ...
In this paper we consider a Proper Generalized Decomposition method to solve the steady incompressible Navier–Stokes equations with random Reynolds number and forcing term. The aim of such technique is to compute a low-cost reduced basis approximation of t ...
The QR algorithm is the method of choice for computing all eigenvalues of a dense nonsymmetric matrix A. After an initial reduction to Hessenberg form, a QR iteration can be viewed as chasing a small bulge from the top left to the bottom right corner along ...
We propose a dimensionality reducing matrix design based on training data with constraints on its Frobenius norm and number of rows. Our design criteria is aimed at preserving the distances between the data points in the dimensionality reduced space as muc ...
In this report, we use a variety of tools from differential geometry to propose a nonlinear extension of the principal components analysis (PCA) into manifolds setting. This extension, that we shall call principal geodesics analysis (PGA), attempts to find ...