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In a geometric $k$-clustering problem the goal is to partition a set of points in $\mathbb{R}^d$ into $k$ subsets such that a certain cost function of the clustering is minimized. We present data structures for orthogonal range-clustering…

Computational Geometry · Computer Science 2017-05-18 Mikkel Abrahamsen , Mark de Berg , Kevin Buchin , Mehran Mehr , Ali D. Mehrabi

Clustering ensemble, or consensus clustering, has emerged as a powerful tool for improving both the robustness and the stability of results from individual clustering methods. Weighted clustering ensemble arises naturally from clustering…

Computer Vision and Pattern Recognition · Computer Science 2021-12-14 Mimi Zhang

Center-based clustering is a pivotal primitive for unsupervised learning and data analysis. A popular variant is undoubtedly the k-means problem, which, given a set $P$ of points from a metric space and a parameter $k<|P|$, requires to…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-02-21 Enrico Dandolo , Andrea Pietracaprina , Geppino Pucci

We study the complexity of the classic capacitated k-median and k-means problems parameterized by the number of centers, k. These problems are notoriously difficult since the best known approximation bound for high dimensional Euclidean…

Data Structures and Algorithms · Computer Science 2022-08-31 Vincent Cohen-Addad , Jason Li

$k$-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

Kernel $k$-means clustering can correctly identify and extract a far more varied collection of cluster structures than the linear $k$-means clustering algorithm. However, kernel $k$-means clustering is computationally expensive when the…

Machine Learning · Computer Science 2019-02-12 Shusen Wang , Alex Gittens , Michael W. Mahoney

In the era of big data, k-means clustering has been widely adopted as a basic processing tool in various contexts. However, its computational cost could be prohibitively high as the data size and the cluster number are large. It is well…

Machine Learning · Computer Science 2017-05-05 Cheng-Hao Deng , Wan-Lei Zhao

Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-10-10 Marco Jacopo Ferrarotti , Sergio Decherchi , Walter Rocchia

We study beyond worst case analysis for the $k$-means problem where the goal is to model typical instances of $k$-means arising in practice. Existing theoretical approaches provide guarantees under certain assumptions on the optimal…

Data Structures and Algorithms · Computer Science 2026-02-03 Poojan Shah , Shashwat Agrawal , Ragesh Jaiswal

Given a set of points, clustering consists of finding a partition of a point set into $k$ clusters such that the center to which a point is assigned is as close as possible. Most commonly, centers are points themselves, which leads to the…

Machine Learning · Computer Science 2023-10-16 Maria Sofia Bucarelli , Matilde Fjeldsø Larsen , Chris Schwiegelshohn , Mads Bech Toftrup

The widely applied k-means algorithm produces clusterings that violate our expectations with respect to high/low similarity/density and is in conflict with Kleinberg's axiomatic system for distance based clustering algorithms that…

Machine Learning · Computer Science 2023-08-08 Mieczysław A. Kłopotek

The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is traditionally considered an unsupervised learning task. In recent years, the use of background knowledge to improve the cluster quality and promote…

Optimization and Control · Mathematics 2022-07-26 Veronica Piccialli , Anna Russo Russo , Antonio M. Sudoso

We propose a new clustering algorithm that is robust to the presence of outliers in the dataset. We perform Lloyd-type iterations with robust estimates of the centroids. More precisely, we build on the idea of median-of-means statistics to…

Methodology · Statistics 2020-08-20 Camille Brunet-Saumard , Edouard Genetay , Adrien Saumard

Minimum sum-of-squares clustering (MSSC) is a widely used clustering model, of which the popular K-means algorithm constitutes a local minimizer. It is well known that the solutions of K-means can be arbitrarily distant from the true MSSC…

Machine Learning · Computer Science 2018-12-21 Daniel Gribel , Thibaut Vidal

Existing approaches remain largely constrained by traditional distance metrics, limiting their effectiveness in handling random data. In this work, we introduce the first k-means variant in the literature that operates within a…

Distributed data mining techniques and mainly distributed clustering are widely used in the last decade because they deal with very large and heterogeneous datasets which cannot be gathered centrally. Current distributed clustering…

Databases · Computer Science 2018-02-02 Malika Bendechache , M-Tahar Kechadi

We show that the objective function of conventional k-means clustering can be expressed as the Frobenius norm of the difference of a data matrix and a low rank approximation of that data matrix. In short, we show that k-means clustering is…

Machine Learning · Statistics 2015-12-24 Christian Bauckhage

The $k$-means clustering algorithm and its variant, the spherical $k$-means clustering, are among the most important and popular methods in unsupervised learning and pattern detection. In this paper, we explore how the spherical $k$-means…

Methodology · Statistics 2019-05-28 Anja Janßen , Phyllis Wan

One of the most prominent challenges in clustering is "the user's dilemma," which is the problem of selecting an appropriate clustering algorithm for a specific task. A formal approach for addressing this problem relies on the…

Machine Learning · Computer Science 2016-10-05 Margareta Ackerman , Shai Ben-David , Simina Brânzei , David Loker

Clustering is one of the most fundamental tools in the artificial intelligence area, particularly in the pattern recognition and learning theory. In this paper, we propose a simple, but novel approach for variance-based k-clustering tasks,…

Machine Learning · Computer Science 2020-09-17 Yicheng Xu , Vincent Chau , Chenchen Wu , Yong Zhang , Vassilis Zissimopoulos , Yifei Zou