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Reduced k-means clustering is a method for clustering objects in a low-dimensional subspace. The advantage of this method is that both clustering of objects and low-dimensional subspace reflecting the cluster structure are simultaneously…

Statistics Theory · Mathematics 2014-02-14 Yoshikazu Terada

In this paper, we study the strong consistency of the sparse K-means clustering for high dimensional data. We prove the consistency in both risk and clustering for the Euclidean distance. We discuss the characterization of the limit of the…

Statistics Theory · Mathematics 2025-04-15 Jeungju Kim , Johan Lim

The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that…

Data Structures and Algorithms · Computer Science 2018-04-26 Allan Grønlund , Kasper Green Larsen , Alexander Mathiasen , Jesper Sindahl Nielsen , Stefan Schneider , Mingzhou Song

The classical center based clustering problems such as $k$-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise…

Data Structures and Algorithms · Computer Science 2015-04-13 Anup Bhattacharya , Ragesh Jaiswal , Amit Kumar

The $k$-means algorithm is one of the most widely used clustering heuristics. Despite its simplicity, analyzing its running time and quality of approximation is surprisingly difficult and can lead to deep insights that can be used to…

Data Structures and Algorithms · Computer Science 2016-02-29 Johannes Blömer , Christiane Lammersen , Melanie Schmidt , Christian Sohler

The K-means algorithm is one of the most widely studied clustering algorithms in machine learning. While extensive research has focused on its ability to achieve a globally optimal solution, there still lacks a rigorous analysis of its…

Machine Learning · Computer Science 2025-06-12 Mingyi Li , Michael R. Metel , Akiko Takeda

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…

Machine Learning · Statistics 2022-08-26 Zhaoqiang Liu , Vincent Y. F. Tan

We propose a robust clustering framework for high-dimensional data with heavy tails and a large fraction of irrelevant variables. The method replaces the mean updates of Lloyd's $K$-means with \emph{spatial medians} to enhance robustness.…

Methodology · Statistics 2026-05-04 Ping Zhao , Dan Zhuang , Long Feng

The k-means algorithm is a well-known method for partitioning n points that lie in the d-dimensional space into k clusters. Its main features are simplicity and speed in practice. Theoretically, however, the best known upper bound on its…

Computational Geometry · Computer Science 2008-12-03 Andrea Vattani

The $K$-means algorithm is extended to allow for partitioning of skewed groups. Our algorithm is called TiK-Means and contributes a $K$-means type algorithm that assigns observations to groups while estimating their skewness-transformation…

Machine Learning · Statistics 2019-05-21 Nicholas S. Berry , Ranjan Maitra

The $k$-means problem is a classic objective for modeling clustering in a metric space. Given a set of points in a metric space, the goal is to find $k$ representative points so as to minimize the sum of the squared distances from each…

Computational Geometry · Computer Science 2026-03-31 Vincent Cohen-Addad , Karthik C. S. , David Saulpic , Chris Schwiegelshohn

Distributed Computation has been a recent trend in engineering research. Parallel Computation is widely used in different areas of Data Mining, Image Processing, Simulating Models, Aerodynamics and so forth. One of the major usage of…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-03-28 C Rashmi

Clustering non-Euclidean data is difficult, and one of the most used algorithms besides hierarchical clustering is the popular algorithm Partitioning Around Medoids (PAM), also simply referred to as k-medoids clustering. In Euclidean…

Machine Learning · Computer Science 2024-07-08 Erich Schubert , Peter J. Rousseeuw

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 study (Euclidean) $k$-median and $k$-means with constraints in the streaming model. There have been recent efforts to design unified algorithms to solve constrained $k$-means problems without using knowledge of the specific constraint at…

Data Structures and Algorithms · Computer Science 2021-06-15 Melanie Schmidt , Julian Wargalla

In this paper, we investigate the learning-augmented $k$-median clustering problem, which aims to improve the performance of traditional clustering algorithms by preprocessing the point set with a predictor of error rate $\alpha \in [0,1)$.…

Data Structures and Algorithms · Computer Science 2026-03-12 Kangke Cheng , Shihong Song , Guanlin Mo , Hu Ding

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 propose k^2-means, a new clustering method which efficiently copes with large numbers of clusters and achieves low energy solutions. k^2-means builds upon the standard k-means (Lloyd's algorithm) and combines a new strategy to accelerate…

Machine Learning · Computer Science 2016-05-31 Eirikur Agustsson , Radu Timofte , Luc Van Gool

In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is…

Machine Learning · Computer Science 2014-06-17 Weiran Wang , Miguel Á. Carreira-Perpiñán

This paper considers the well-studied algorithmic regime of designing a $(1+\epsilon)$-approximation algorithm for a $k$-clustering problem that runs in time $f(k,\epsilon)poly(n)$ (sometimes called an efficient parameterized approximation…