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Feature subset selection, as a special case of the general subset selection problem, has been the topic of a considerable number of studies due to the growing importance of data-mining applications. In the feature subset selection problem…

Machine Learning · Computer Science 2014-11-13 Tofigh Naghibi , Sarah Hoffmann , Beat Pfister

One of the main applications of semidefinite programming lies in linear systems and control theory. Many problems in this subject, certainly the textbook classics, have matrices as variables, and the formulas naturally contain…

Operator Algebras · Mathematics 2011-12-30 J. William Helton , Igor Klep , Scott McCullough

We present a data-structure for orthogonal range searching for random points in the plane. The new data-structure uses (in expectation) $O\bigl(n \log n ( \log \log n)^2 \bigr)$ space, and answers emptiness queries in constant time. As a…

Computational Geometry · Computer Science 2025-05-12 Jonathan E. Dullerud , Sariel Har-Peled

In this paper we discuss a classical geometrical problem of estimating an unknown point's location in $\Real{n}$ from several noisy measurements of the Euclidean distances from this point to a set of known reference points (anchors). We…

Computational Engineering, Finance, and Science · Computer Science 2026-03-06 Giuseppe C. Calafiore

We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…

Machine Learning · Computer Science 2023-08-08 Jonathan A. Kelner , Jerry Li , Allen Liu , Aaron Sidford , Kevin Tian

Let $P$ be a set of $m$ points in ${\mathbb R}^2$, let $\Sigma$ be a set of $n$ semi-algebraic sets of constant complexity in ${\mathbb R}^2$, let $(S,+)$ be a semigroup, and let $w: P \rightarrow S$ be a weight function on the points of…

Computational Geometry · Computer Science 2024-09-17 Pankaj K. Agarwal , Esther Ezra , Micha Sharir

This paper studies the \emph{$\varepsilon$-approximate range emptiness} problem, where the task is to represent a set $S$ of $n$ points from $\{0,\ldots,U-1\}$ and answer emptiness queries of the form "$[a ; b]\cap S \neq \emptyset$ ?" with…

Data Structures and Algorithms · Computer Science 2014-07-11 Mayank Goswami , Allan Grønlund , Kasper Green Larsen , Rasmus Pagh

We give a simplified and improved lower bound for the simplex range reporting problem. We show that given a set $P$ of $n$ points in $\mathbb{R}^d$, any data structure that uses $S(n)$ space to answer such queries must have…

Computational Geometry · Computer Science 2022-10-27 Peyman Afshani , Pingan Cheng

We revisit the range sampling problem: the input is a set of points where each point is associated with a real-valued weight. The goal is to store them in a structure such that given a query range and an integer $k$, we can extract $k$…

Data Structures and Algorithms · Computer Science 2019-03-20 Peyman Afshani , Jeff M. Phillips

Remote sensing data is crucial for applications ranging from monitoring forest fires and deforestation to tracking urbanization. Most of these tasks require dense pixel-level annotations for the model to parse visual information from…

Computer Vision and Pattern Recognition · Computer Science 2021-10-18 Shasvat Desai , Debasmita Ghose

The concept of \emph{data depth} in non-parametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. \emph{Halfspace depth} is a measure of data depth. Given a set $S$ of points…

Computational Geometry · Computer Science 2009-10-13 David Bremner , Dan Chen

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The…

Machine Learning · Computer Science 2011-02-01 Gilles Meyer , Silvere Bonnabel , Rodolphe Sepulchre

Dedicated treatment of symmetries in satisfiability problems (SAT) is indispensable for solving various classes of instances arising in practice. However, the exploitation of symmetries usually takes a black box approach. Typically,…

Data Structures and Algorithms · Computer Science 2024-01-02 Markus Anders , Pascal Schweitzer , Mate Soos

The concept of data depth in non-parametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. Halfspace depth is a measure of data depth. Given a set S of points and a point p, the…

Computational Geometry · Computer Science 2007-05-23 Dan Chen

The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…

Machine Learning · Computer Science 2014-12-01 Vassilis Kalofolias , Xavier Bresson , Michael Bronstein , Pierre Vandergheynst

This paper presents generalizations of semidefinite programming formulations of 1-norm optimization problems over infinite dictionaries of vectors of complex exponentials, which were recently proposed for superresolution, gridless…

Optimization and Control · Mathematics 2016-04-12 Hsiao-Han Chao , Lieven Vandenberghe

We extend Random Access, a fundamental operation that enables efficient search and exploration algorithms, to the modern interactive data systems based on Ranked Retrieval and Similarity Search, where orderings are dynamically defined over…

Data Structures and Algorithms · Computer Science 2026-05-26 Mohsen Dehghankar , Abolfazl Asudeh , Raghav Mittal , Suraj Shetiya , Gautam Das

Given a dataset $S$ of points in $\mathbb{R}^2$, the range closest-pair (RCP) problem aims to preprocess $S$ into a data structure such that when a query range $X$ is specified, the closest-pair in $S \cap X$ can be reported efficiently.…

Computational Geometry · Computer Science 2018-04-03 Jie Xue , Yuan Li , Saladi Rahul , Ravi Janardan

A fundamental challenge to sensory processing tasks in perception and robotics is the problem of obtaining data associations across views. We present a robust solution for ascertaining potentially dense surface patch (superpixel)…

Computer Vision and Pattern Recognition · Computer Science 2014-11-18 Rahul Sawhney , Fuxin Li , Henrik I. Christensen

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the…

Optimization and Control · Mathematics 2013-04-26 B. Mishra , G. Meyer , R. Sepulchre