Related papers: Uniform projection designs under the stratified $L…
We consider the problem of approximating the unknown density $u\in L^2(\Omega,\lambda)$ of a measure $\mu$ on $\Omega\subset\R^n$, absolutely continuous with respect to some given reference measure $\lambda$, from the only knowledge of…
We compare the essential properties of projections in the L2 and L1 normed spaces by two methods: Projection operators and by minimization of the distance. In Euclidean geometry the orthogonality (L2- conjugacy) plays central role; while in…
This paper presents an enhanced version of our previous work, hybrid non-uniform subdivision surfaces [19], to achieve optimal convergence rates in isogeometric analysis. We introduce a parameter $\lambda$ ($\frac{1}{4}<\lambda<1$) to…
It is now generally accepted that Euclidean-based metrics may not always adequately represent the subjective judgement of a human observer. As a result, many image processing methodologies have been recently extended to take advantage of…
In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…
We consider the problem of digitalizing Euclidean segments. Specifically, we look for a constructive method to connect any two points in $\mathbb{Z}^d$. The construction must be {\em consistent} (that is, satisfy the natural extension of…
Modeling real processes often results in several suitable models. In order to be able to distinguish, or discriminate, which model best represents a phenomenon, one is interested, e.g., in so-called T-optimal designs. These consist of the…
The local intrinsic dimension (LID) of data is a fundamental quantity in signal processing and learning theory, but quantifying the LID of high-dimensional, complex data has been a historically challenging task. Recent works have discovered…
This work develops a sparse and outlier-insensitive method to fit a one-dimensional subspace that can be used as a replacement for eigenvector methods such as principal component analysis (PCA). The method is insensitive to outlier…
A design is a finite set of points in a space on which every "simple" functions averages to its global mean. Illustrative examples of simple functions are low-degree polynomials on the Euclidean sphere or on the Hamming cube. We prove lower…
Spherical or omni-directional images offer an immersive visual format appealing to a wide range of computer vision applications. However, geometric properties of spherical images pose a major challenge for models and metrics designed for…
In this note, we develop fast and deterministic dimensionality reduction techniques for a family of subspace approximation problems. Let $P\subset \mathbbm{R}^N$ be a given set of $M$ points. The techniques developed herein find an $O(n…
In this article, for generalized projective spaces with any weights, we prove four main theorems in three different contexts where the Unital Set Condition USC (Definition $2.8$) on ideals is further examined. In the first context we prove,…
Experimental designs for a generalized linear model (GLM) often depend on the specification of the model, including the link function, the predictors, and unknown parameters, such as the regression coefficients. To deal with uncertainties…
This paper introduces a stratification framework for nonlinear semidefinite programming (NLSDP) that reveals and utilizes the geometry behind the nonsmooth KKT system. Based on the \emph{index stratification} of $\mathbb{S}^n$ and its lift…
In this paper, we present a progressive and iterative approximation method with memory for least square fitting(MLSPIA). It adjusts the control points and the weighted sums iteratively to construct a series of fitting curves (surfaces) with…
The unit-modulus least squares (UMLS) problem has a wide spectrum of applications in signal processing, e.g., phase-only beamforming, phase retrieval, radar code design, and sensor network localization. Scalable first-order methods such as…
Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories:…
Linear fixed point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations. We study methods that use a collection of random…
This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a…