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Cost functions for non-hierarchical pairwise clustering are introduced, in the probabilistic autoencoder framework, by the request of maximal average similarity between the input and the output of the autoencoder. The partition provided by…

Disordered Systems and Neural Networks · Physics 2009-11-07 L. Angelini , L. Nitti , M. Pellicoro , S. Stramaglia

In 2015, Driemel, Krivo\v{s}ija and Sohler introduced the $(k,\ell)$-median problem for clustering polygonal curves under the Fr\'echet distance. Given a set of input curves, the problem asks to find $k$ median curves of at most $\ell$…

Computational Geometry · Computer Science 2020-11-04 Maike Buchin , Anne Driemel , Dennis Rohde

Clustering is considered a non-supervised learning setting, in which the goal is to partition a collection of data points into disjoint clusters. Often a bound $k$ on the number of clusters is given or assumed by the practitioner. Many…

Machine Learning · Computer Science 2012-02-01 Nir Ailon , Ron Begleiter

The K-Means clustering using LLoyd's algorithm is an iterative approach to partition the given dataset into K different clusters. The algorithm assigns each point to the cluster based on the following objective function \[\ \min…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-05-21 Ashish Srivastava , Mohammed Nawfal

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

In all state-of-the-art sketching and coreset techniques for clustering, as well as in the best known fixed-parameter tractable approximation algorithms, randomness plays a key role. For the classic $k$-median and $k$-means problems, there…

Data Structures and Algorithms · Computer Science 2023-10-09 Vincent Cohen-Addad , David Saulpic , Chris Schwiegelshohn

One important tool is the optimal clustering of data into useful categories. Dividing similar objects into a smaller number of clusters is of importance in many applications. These include search engines, monitoring of academic performance,…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-09-21 Gavriel Yarmish , Philip Listowsky , Simon Dexter

Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…

Data Structures and Algorithms · Computer Science 2025-11-25 Jan Eube , Heiko Röglin

Clustering is a commonplace problem in many areas of data science, with applications in biology and bioinformatics, understanding chemical structure, image segmentation, building recommender systems, and many more fields. While there are…

Numerical Analysis · Mathematics 2023-12-25 Tareq Zaman , Nicolas Nytko , Ali Taghibakhshi , Scott MacLachlan , Luke Olson , Matthew West

Software-defined networks (SDNs) are a huge evolution in simplifying implementation and network operation which have reduced costs and made the network programmable. Although SDNs are a suitable option for solving some of the previous…

Networking and Internet Architecture · Computer Science 2019-10-03 Mahdi Sarbazi , Mehdi SadeghZadeh , seyyed Javad Mir Abedini

Clustering is one of the most common unsupervised learning tasks in machine learning and data mining. Clustering algorithms have been used in a plethora of applications across several scientific fields. However, there has been limited…

Machine Learning · Computer Science 2017-02-09 Quang N. Tran , Ba-Ngu Vo , Dinh Phung , Ba-Tuong Vo

\textit{Clustering problems} often arise in the fields like data mining, machine learning etc. to group a collection of objects into similar groups with respect to a similarity (or dissimilarity) measure. Among the clustering problems,…

Computational Geometry · Computer Science 2015-12-10 Sayan Bandyapadhyay , Kasturi Varadarajan

Clustering is a fundamental problem, aiming to partition a set of elements, like agents or data points, into clusters such that elements in the same cluster are closer to each other than to those in other clusters. In this paper, we present…

Multiagent Systems · Computer Science 2026-05-26 Saar Cohen

The Lloyd-Max algorithm is a classical approach to perform K-means clustering. Unfortunately, its cost becomes prohibitive as the training dataset grows large. We propose a compressive version of K-means (CKM), that estimates cluster…

Machine Learning · Computer Science 2017-02-13 Nicolas Keriven , Nicolas Tremblay , Yann Traonmilin , Rémi Gribonval

We study streaming algorithms for Correlation Clustering. Given a graph as an arbitrary-order stream of edges, with each edge labeled as positive or negative, the goal is to partition the vertices into disjoint clusters, such that the…

Data Structures and Algorithms · Computer Science 2025-10-14 Yinhao Dong , Shan Jiang , Shi Li , Pan Peng

Graph coloring is fundamental to distributed computing. We give the first sub-logarithmic distributed algorithm for coloring cluster graphs. These graphs are obtained from the underlying communication network by contracting nodes and edges,…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-06-17 Maxime Flin , Magnus M. Halldorsson , Alexandre Nolin

Clustering is one of the most fundamental problems in data analysis and it has been studied extensively in the literature. Though many clustering algorithms have been proposed, clustering theories that justify the use of these clustering…

Machine Learning · Computer Science 2016-02-22 Cheng-Shang Chang , Wanjiun Liao , Yu-Sheng Chen , Li-Heng Liou

We provide a new bi-criteria $\tilde{O}(\log^2 k)$ competitive algorithm for explainable $k$-means clustering. Explainable $k$-means was recently introduced by Dasgupta, Frost, Moshkovitz, and Rashtchian (ICML 2020). It is described by an…

Machine Learning · Computer Science 2022-04-28 Konstantin Makarychev , Liren Shan

We show that both clustering and subspace embeddings can be performed in the streaming model with the same asymptotic efficiency as in the central/offline setting. For $(k, z)$-clustering in the streaming model, we achieve a number of words…

Data Structures and Algorithms · Computer Science 2025-04-24 Vincent Cohen-Addad , Liudeng Wang , David P. Woodruff , Samson Zhou

This paper shows for the first time that distributed computing can be both reliable and efficient in an environment that is both highly dynamic and hostile. More specifically, we show how to maintain clusters of size $O(\log N)$, each…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-05-17 Rachid Guerraoui , Florian Huc , Anne-Marie Kermarrec