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We present algorithms for the computation of $\varepsilon$-coresets for $k$-median clustering of point sequences in $\mathbb{R}^d$ under the $p$-dynamic time warping (DTW) distance. Coresets under DTW have not been investigated before, and…

Computational Geometry · Computer Science 2024-03-08 Jacobus Conradi , Benedikt Kolbe , Ioannis Psarros , Dennis Rohde

Energy load balancing is an essential issue in designing wireless sensor networks (WSNs). Clustering techniques are utilized as energy-efficient methods to balance the network energy and prolong its lifetime. In this paper, we propose an…

Systems and Control · Electrical Eng. & Systems 2024-03-26 Botao Zhu , Ebrahim Bedeer , Ha H. Nguyen , Robert Barton , Jerome Henry

Coresets are modern data-reduction tools that are widely used in data analysis to improve efficiency in terms of running time, space and communication complexity. Our main result is a fast algorithm to construct a small coreset for k-Median…

Data Structures and Algorithms · Computer Science 2020-07-16 Vladimir Braverman , Shaofeng H. -C. Jiang , Robert Krauthgamer , Xuan Wu

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 investigate $k$-means clustering in the online no-substitution setting when the input arrives in \emph{arbitrary} order. In this setting, points arrive one after another, and the algorithm is required to instantly decide whether to take…

Data Structures and Algorithms · Computer Science 2023-01-19 Robi Bhattacharjee , Michal Moshkovitz

The widespread adoption of smart meters for monitoring energy consumption has generated vast quantities of high-resolution time series data which remains underutilised. While clustering has emerged as a fundamental tool for mining smart…

The clustering problem, in its many variants, has numerous applications in operations research and computer science (e.g., in applications in bioinformatics, image processing, social network analysis, etc.). As sizes of data sets have grown…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-10-24 Sayan Bandyapadhyay , Tanmay Inamdar , Shreyas Pai , Sriram V. Pemmaraju

Clustering is an essential task to unsupervised learning. It tries to automatically separate instances into coherent subsets. As one of the most well-known clustering algorithms, k-means assigns sample points at the boundary to a unique…

Machine Learning · Computer Science 2022-02-22 Sixiao Zheng , Ke Fan , Yanxi Hou , Jianfeng Feng , Yanwei Fu

$k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains…

Quantum Physics · Physics 2023-06-06 Yecheng Xue , Xiaoyu Chen , Tongyang Li , Shaofeng H. -C. Jiang

This paper considers a movement minimization problem for mobile sensors. Given a set of $n$ point targets, the $k$-Sink Minimum Movement Target Coverage Problem is to schedule mobile sensors, initially located at $k$ base stations, to cover…

Computational Geometry · Computer Science 2023-05-09 Nonthaphat Wongwattanakij , Nattawut Phetmak , Chaiporn Jaikaeo , Jittat Fakcharoenphol

Recent spectral clustering methods are a propular and powerful technique for data clustering. These methods need to solve the eigenproblem whose computational complexity is $O(n^3)$, where $n$ is the number of data samples. In this paper, a…

Machine Learning · Computer Science 2007-11-26 Chunjing Xu , Jianzhuang Liu , Xiaoou Tang

We study the problem of constructing $\varepsilon$-coresets for the $(k, z)$-clustering problem in a doubling metric $M(X, d)$. An $\varepsilon$-coreset is a weighted subset $S\subseteq X$ with weight function $w : S \rightarrow…

Data Structures and Algorithms · Computer Science 2018-08-21 Lingxiao Huang , Shaofeng H. -C. Jiang , Jian Li , Xuan Wu

For a set of points in $\mathbb{R}^d$, the Euclidean $k$-means problems consists of finding $k$ centers such that the sum of distances squared from each data point to its closest center is minimized. Coresets are one the main tools…

Data Structures and Algorithms · Computer Science 2023-10-30 Monika Henzinger , David Saulpic , Leonhard Sidl

A set of points $P$ in a metric space and a constant integer $k$ are given. The $k$-center problem finds $k$ points as centers among $P$, such that the maximum distance of any point of $P$ to their closest centers $(r)$ is minimized.…

Data Structures and Algorithms · Computer Science 2019-04-25 Sepideh Aghamolaei , Mohammad Ghodsi

We present a unified framework that yields EPASes for constrained $(k,z)$-clustering in metric spaces of bounded (algorithmic) scatter dimension, a notion introduced by Abbasi et al. (FOCS 2023). They showed that several well known metric…

Data Structures and Algorithms · Computer Science 2026-02-10 Sujoy Bhore , Ameet Gadekar , Tanmay Inamdar

This paper describes a method for clustering data that are spread out over large regions and which dimensions are on different scales of measurement. Such an algorithm was developed to implement a robotics application consisting in sorting…

Machine Learning · Computer Science 2017-03-23 Joris Guérin , Olivier Gibaru , Stéphane Thiery , Eric Nyiri

Mining clusters from data is an important endeavor in many applications. The $k$-means method is a popular, efficient, and distribution-free approach for clustering numerical-valued data, but does not apply for categorical-valued…

Methodology · Statistics 2021-08-24 Karin S. Dorman , Ranjan Maitra

The $k$-means algorithm is often used in clustering applications but its usage requires a complete data matrix. Missing data, however, is common in many applications. Mainstream approaches to clustering missing data reduce the missing data…

Computation · Statistics 2018-06-07 Jocelyn T. Chi , Eric C. Chi , Richard G. Baraniuk

This paper studies the fair range clustering problem in which the data points are from different demographic groups and the goal is to pick $k$ centers with the minimum clustering cost such that each group is at least minimally represented…

Machine Learning · Computer Science 2023-06-23 Sèdjro S. Hotegni , Sepideh Mahabadi , Ali Vakilian

The k-means algorithm can simplify large-scale spatial vectors, such as 2D geo-locations and 3D point clouds, to support fast analytics and learning. However, when processing large-scale datasets, existing k-means algorithms have been…

Machine Learning · Computer Science 2024-12-04 Yushuai Ji , Zepeng Liu , Sheng Wang , Yuan Sun , Zhiyong Peng