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We initiate the study of coresets for clustering in graph metrics, i.e., the shortest-path metric of edge-weighted graphs. Such clustering problems are essential to data analysis and used for example in road networks and data visualization.…

Data Structures and Algorithms · Computer Science 2022-12-13 Daniel Baker , Vladimir Braverman , Lingxiao Huang , Shaofeng H. -C. Jiang , Robert Krauthgamer , Xuan Wu

Bayesian coresets approximate a posterior distribution by building a small weighted subset of the data points. Any inference procedure that is too computationally expensive to be run on the full posterior can instead be run inexpensively on…

Machine Learning · Statistics 2023-01-18 Cian Naik , Judith Rousseau , Trevor Campbell

In projective clustering we are given a set of n points in $R^d$ and wish to cluster them to a set $S$ of $k$ linear subspaces in $R^d$ according to some given distance function. An $\eps$-coreset for this problem is a weighted (scaled)…

Data Structures and Algorithms · Computer Science 2020-11-30 Adiel Statman , Liat Rozenberg , Dan Feldman

An $\varepsilon$-coreset for Least-Mean-Squares (LMS) of a matrix $A\in{\mathbb{R}}^{n\times d}$ is a small weighted subset of its rows that approximates the sum of squared distances from its rows to every affine $k$-dimensional subspace of…

Machine Learning · Computer Science 2019-07-03 Alaa Maalouf , Adiel Statman , Dan Feldman

We study the problem of constructing coresets for $(k, z)$-clustering when the input dataset is corrupted by stochastic noise drawn from a known distribution. In this setting, evaluating the quality of a coreset is inherently challenging,…

Machine Learning · Computer Science 2025-10-28 Lingxiao Huang , Zhize Li , Nisheeth K. Vishnoi , Runkai Yang , Haoyu Zhao

Clustering is the task of partitioning a given set of geometric objects. This is thoroughly studied when the objects are points in the euclidean space. There are also several approaches for points in general metric spaces. In this thesis we…

Computational Geometry · Computer Science 2019-11-07 Dennis Rohde

A coreset is a small set that can approximately preserve the structure of the original input data set. Therefore we can run our algorithm on a coreset so as to reduce the total computational complexity. Conventional coreset techniques…

Machine Learning · Computer Science 2022-10-11 Jiaxiang Chen , Qingyuan Yang , Ruomin Huang , Hu Ding

In a number of situations, collecting a function value for every data point may be prohibitively expensive, and random sampling ignores any structure in the underlying data. We introduce a scalable optimization algorithm with no correction…

Machine Learning · Computer Science 2020-06-23 Saeed Vahidian , Baharan Mirzasoleiman , Alexander Cloninger

In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…

Data Structures and Algorithms · Computer Science 2025-04-30 Aditya Bhaskara , Sepideh Mahabadi , Madhusudhan Reddy Pittu , Ali Vakilian , David P. Woodruff

Coresets for $k$-means and $k$-median problems yield a small summary of the data, which preserve the clustering cost with respect to any set of $k$ centers. Recently coresets have also been constructed for constrained $k$-means and…

Data Structures and Algorithms · Computer Science 2023-05-29 Ragesh Jaiswal , Amit Kumar

We design and mathematically analyze sampling-based algorithms for regularized loss minimization problems that are implementable in popular computational models for large data, in which the access to the data is restricted in some way. Our…

Machine Learning · Computer Science 2019-06-04 Ryan R. Curtin , Sungjin Im , Ben Moseley , Kirk Pruhs , Alireza Samadian

We present an efficient coresets-based neural network compression algorithm that sparsifies the parameters of a trained fully-connected neural network in a manner that provably approximates the network's output. Our approach is based on an…

Machine Learning · Computer Science 2019-05-21 Cenk Baykal , Lucas Liebenwein , Igor Gilitschenski , Dan Feldman , Daniela Rus

Fair clustering is a constrained variant of clustering where the goal is to partition a set of colored points, such that the fraction of points of any color in every cluster is more or less equal to the fraction of points of this color in…

Data Structures and Algorithms · Computer Science 2020-07-21 Sayan Bandyapadhyay , Fedor V. Fomin , Kirill Simonov

We study the problem of constructing coresets for clustering problems with time series data. This problem has gained importance across many fields including biology, medicine, and economics due to the proliferation of sensors facilitating…

Machine Learning · Computer Science 2021-10-29 Lingxiao Huang , K. Sudhir , Nisheeth K. Vishnoi

Designing small-sized \emph{coresets}, which approximately preserve the costs of the solutions for large datasets, has been an important research direction for the past decade. We consider coreset construction for a variety of general…

Data Structures and Algorithms · Computer Science 2024-10-11 Lingxiao Huang , Jian Li , Pinyan Lu , Xuan Wu

Clustering is an important technique for identifying structural information in large-scale data analysis, where the underlying dataset may be too large to store. In many applications, recent data can provide more accurate information and…

Data Structures and Algorithms · Computer Science 2023-11-02 David P. Woodruff , Peilin Zhong , Samson Zhou

Coreset (or core-set) is a small weighted \emph{subset} $Q$ of an input set $P$ with respect to a given \emph{monotonic} function $f:\mathbb{R}\to\mathbb{R}$ that \emph{provably} approximates its fitting loss $\sum_{p\in P}f(p\cdot x)$ to…

Machine Learning · Computer Science 2021-12-24 Elad Tolochinsky , Ibrahim Jubran , Dan Feldman

Coreset Selection (CS) aims to identify a subset of the training dataset that achieves model performance comparable to using the entire dataset. Many state-of-the-art CS methods select coresets using scores whose computation requires…

Machine Learning · Computer Science 2025-06-05 Akshay Mehra , Trisha Mittal , Subhadra Gopalakrishnan , Joshua Kimball

We investigate coresets - succinct, small summaries of large data sets - so that solutions found on the summary are provably competitive with solution found on the full data set. We provide an overview over the state-of-the-art in coreset…

Machine Learning · Statistics 2017-06-06 Olivier Bachem , Mario Lucic , Andreas Krause

Radial basis function neural networks (\emph{RBFNN}) are {well-known} for their capability to approximate any continuous function on a closed bounded set with arbitrary precision given enough hidden neurons. In this paper, we introduce the…

Machine Learning · Computer Science 2023-03-10 Murad Tukan , Samson Zhou , Alaa Maalouf , Daniela Rus , Vladimir Braverman , Dan Feldman