Simultaneous Approximation of Polynomials

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Publications associées (29)

Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms

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Clustering is a classic topic in optimization with k-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best-known algorithm for k-means in Euclidean space with a provable guarantee is a simple local ...

SIAM PUBLICATIONS2020

Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance case

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We consider the problem of finding an optimal transport plan between an absolutely continuous measure and a finitely supported measure of the same total mass when the transport cost is the unsquared Euclidean distance. We may think of this problem as close ...

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Coordinate Difference Matrices

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In many problems such as phase retrieval, molecular biology, source localization, and sensor array calibration, one can measure vector differences between pairs of points and attempt to recover the position of these points; this class of problems is called ...

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From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

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Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful ...

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Humans exhibit outstanding learning and adaptation capabilities while performing various types of manipulation tasks. When learning new skills, humans are able to extract important information by observing examples of a task and efficiently refine a priori ...

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On some graph-based two-sample tests for high dimension, low sample size data

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Testing for equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been proposed in the literature, ...

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On Perfect Clustering of High Dimension, Low Sample Size Data

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Popular clustering algorithms based on usual distance functions (e.g., the Euclidean distance) often suffer in high dimension, low sample size (HDLSS) situations, where concentration of pairwise distances and violation of neighborhood structure have advers ...

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We present new techniques to analyze natural local search algorithms for several variants of the max-sum diversification problem which, in its most basic form, is as follows: given an n-point set X subset of R-d and an integer k, select k points in X so th ...

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Volumetric untrimming: Precise decomposition of trimmed trivariates into tensor products

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3D objects, modeled using Computer Aided Geometric Design (CAGD) tools, are traditionally represented using a boundary representation (B-rep), and typically use spline functions to parameterize these boundary surfaces. However, recent development in physic ...

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