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Related papers: Coresets for Triangulation

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Given a set $F$ of $n$ positive functions over a ground set $X$, we consider the problem of computing $x^*$ that minimizes the expression $\sum_{f\in F}f(x)$, over $x\in X$. A typical application is \emph{shape fitting}, where we wish to…

Machine Learning · Computer Science 2016-05-31 Dan Feldman , Michael Langberg

We study the accuracy of triangulation in multi-camera systems with respect to the number of cameras. We show that, under certain conditions, the optimal achievable reconstruction error decays quadratically as more cameras are added to the…

Computer Vision and Pattern Recognition · Computer Science 2018-04-30 Adam Scholefield , Alireza Ghasemi , Martin Vetterli

We present TRI\`EST, a suite of one-pass streaming algorithms to compute unbiased, low-variance, high-quality approximations of the global and local (i.e., incident to each vertex) number of triangles in a fully-dynamic graph represented as…

Data Structures and Algorithms · Computer Science 2016-06-29 Lorenzo De Stefani , Alessandro Epasto , Matteo Riondato , Eli Upfal

Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have…

Computational Geometry · Computer Science 2010-01-25 Evan VanderZee , Anil N. Hirani , Damrong Guoy , Edgar Ramos

We study efficient algorithms for the Euclidean $k$-Center problem, focusing on the regime of large $k$. We take the approach of data reduction by considering $\alpha$-coreset, which is a small subset $S$ of the dataset $P$ such that any…

Data Structures and Algorithms · Computer Science 2025-02-11 Arnold Filtser , Shaofeng H. -C. Jiang , Yi Li , Anurag Murty Naredla , Ioannis Psarros , Qiaoyuan Yang , Qin Zhang

Given a set of $n$ points on a plane, in the Minimum Weight Triangulation problem, we wish to find a triangulation that minimizes the sum of Euclidean length of its edges. This incredibly challenging problem has been studied for more than…

Computational Geometry · Computer Science 2017-06-13 Sharath Raghvendra , Mariëtte C. Wessels

3D perception in point clouds is transforming the perception ability of future intelligent machines. Point cloud algorithms, however, are plagued by irregular memory accesses, leading to massive inefficiencies in the memory sub-system,…

Hardware Architecture · Computer Science 2022-04-25 Yu Feng , Gunnar Hammonds , Yiming Gan , Yuhao Zhu

A data filtering method for cluster analysis is proposed, based on minimizing a least squares function with a weighted $\ell_0$-norm penalty. To overcome the discontinuity of the objective function, smooth non-convex functions are employed…

Optimization and Control · Mathematics 2017-05-23 Andrea Cristofari

Previous work showed empirically that large neural networks can be significantly reduced in size while preserving their accuracy. Model compression became a central research topic, as it is crucial for deployment of neural networks on…

Machine Learning · Computer Science 2020-01-06 Ben Mussay , Margarita Osadchy , Vladimir Braverman , Samson Zhou , Dan Feldman

A coreset is a tiny weighted subset of an input set, that closely resembles the loss function, with respect to a certain set of queries. Coresets became prevalent in machine learning as they have shown to be advantageous for many…

Machine Learning · Computer Science 2023-05-23 Alaa Maalouf , Murad Tukan , Vladimir Braverman , Daniela Rus

Cryo-electron microscopy (cryo-EM) has recently emerged as a powerful tool for obtaining three-dimensional (3D) structures of biological macromolecules in native states. A minimum cryo-EM image data set for deriving a meaningful…

Applications · Statistics 2014-04-28 Ting-Li Chen , Dai-Ni Hsieh , Hung Hung , I-Ping Tu , Pei-Shien Wu , Yi-Ming Wu , Wei-Hau Chang , Su-Yun Huang

This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…

Numerical Analysis · Mathematics 2016-08-03 Kristian Bredies , Barbara Kaltenbacher , Elena Resmerita

We study fair clustering problems as proposed by Chierichetti et al. (NIPS 2017). Here, points have a sensitive attribute and all clusters in the solution are required to be balanced with respect to it (to counteract any form of…

Data Structures and Algorithms · Computer Science 2021-03-10 Melanie Schmidt , Chris Schwiegelshohn , Christian Sohler

In a recent work, [19] studied the following "fair" variants of classical clustering problems such as $k$-means and $k$-median: given a set of $n$ data points in $\mathbb{R}^d$ and a binary type associated to each data point, the goal is to…

Data Structures and Algorithms · Computer Science 2019-12-18 Lingxiao Huang , Shaofeng H. -C. Jiang , Nisheeth K. Vishnoi

To improve the efficiency and sustainability of learning deep models, we propose CREST, the first scalable framework with rigorous theoretical guarantees to identify the most valuable examples for training non-convex models, particularly…

Machine Learning · Computer Science 2023-06-05 Yu Yang , Hao Kang , Baharan Mirzasoleiman

In real world, our datasets often contain outliers. Moreover, the outliers can seriously affect the final machine learning result. Most existing algorithms for handling outliers take high time complexities (e.g. quadratic or cubic…

Computational Geometry · Computer Science 2020-02-28 Hu Ding , Zixiu Wang

Efficient global optimization is a widely used method for optimizing expensive black-box functions such as tuning hyperparameter, and designing new material, etc. Despite its popularity, less attention has been paid to analyzing the…

Optimization and Control · Mathematics 2022-09-21 Wenjie Xu , Yuning Jiang , Emilio T. Maddalena , Colin N. Jones

Image triangulation, the practice of decomposing images into triangles, deliberately employs simplification to create an abstracted representation. While triangulating an image is a relatively simple process, difficulties arise when…

Computational Geometry · Computer Science 2024-08-30 Olivia Laske , Lori Ziegelmeier

Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…

Data Structures and Algorithms · Computer Science 2016-11-08 Guilherme D. da Fonseca , Vinícius G. Pereira de Sá , Celina M. H. de Figueiredo

The problem of the minimization of least squares functionals with $\ell^1$ penalties is considered in an infinite dimensional Hilbert space setting. While there are several algorithms available in the finite dimensional setting there are…

Numerical Analysis · Mathematics 2010-10-26 Dirk A. Lorenz