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Related papers: Cluster Editing with Vertex Splitting

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Correlation clustering is a fundamental combinatorial optimization problem arising in many contexts and applications that has been the subject of dozens of papers in the literature. In this problem we are given a general weighted graph…

Data Structures and Algorithms · Computer Science 2019-07-02 Saba Ahmadi , Sainyam Galhotra , Samir Khuller , Barna Saha , Roy Schwartz

We give the first $2$-approximation algorithm for the cluster vertex deletion problem. This is tight, since approximating the problem within any constant factor smaller than $2$ is UGC-hard. Our algorithm combines the previous approaches,…

Combinatorics · Mathematics 2021-10-19 Manuel Aprile , Matthew Drescher , Samuel Fiorini , Tony Huynh

Apart from the role the clustering coefficient plays in the definition of the small-world phenomena, it also has great relevance for practical problems involving networked dynamical systems. To study the impact of the clustering coefficient…

Physics and Society · Physics 2022-07-19 Robert E. Kooij , Nikolaj Horsevad Sørensen , Roland Bouffanais

We consider the classic Correlation Clustering problem: Given a complete graph where edges are labelled either $+$ or $-$, the goal is to find a partition of the vertices that minimizes the number of the \pedges across parts plus the number…

Data Structures and Algorithms · Computer Science 2023-10-02 Vincent Cohen-Addad , Euiwoong Lee , Shi Li , Alantha Newman

Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…

Social and Information Networks · Computer Science 2020-02-19 Ilya Amburg , Nate Veldt , Austin R. Benson

This paper uses the relationship between graph conductance and spectral clustering to study (i) the failures of spectral clustering and (ii) the benefits of regularization. The explanation is simple. Sparse and stochastic graphs create a…

Machine Learning · Statistics 2018-12-04 Yilin Zhang , Karl Rohe

The Cluster Deletion problem takes a graph $G$ as input and asks for a minimum size set of edges $X$ such that $G-X$ is the disjoint union of complete graphs. An equivalent formulation is the Clique Partition problem, which asks to find a…

Data Structures and Algorithms · Computer Science 2025-09-26 Nicola Galesi , Tony Huynh , Fariba Ranjbar

This paper is an extensive survey of literature on complex network communities and clustering. Complex networks describe a widespread variety of systems in nature and society especially systems composed by a large number of highly…

Social and Information Networks · Computer Science 2015-03-24 Biswajit Saha , Amitabha Mandal , Soumendu Bikas Tripathy , Debaprasad Mukherjee

Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…

Machine Learning · Statistics 2016-11-17 Yudong Chen , Sujay Sanghavi , Huan Xu

Traditionally, graph quality metrics focus on readability, but recent studies show the need for metrics which are more specific to the discovery of patterns in graphs. Cluster analysis is a popular task within graph analysis, yet there is…

Data Structures and Algorithms · Computer Science 2019-08-22 Amyra Meidiana , Seok-Hee Hong , Peter Eades , Daniel Keim

Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides…

Machine Learning · Statistics 2017-10-25 Norbert Binkiewicz , Joshua T. Vogelstein , Karl Rohe

Several clustering frameworks with interactive (semi-supervised) queries have been studied in the past. Recently, clustering with same-cluster queries has become popular. An algorithm in this setting has access to an oracle with full…

Data Structures and Algorithms · Computer Science 2019-08-15 Barna Saha , Sanjay Subramanian

Coresets have become an invaluable tool for solving $k$-means and kernel $k$-means clustering problems on large datasets with small numbers of clusters. On the other hand, spectral clustering works well on sparse graphs and has recently…

Machine Learning · Computer Science 2025-03-11 Ben Jourdan , Gregory Schwartzman , Peter Macgregor , He Sun

Clustering large, mixed data is a central problem in data mining. Many approaches adopt the idea of k-means, and hence are sensitive to initialisation, detect only spherical clusters, and require a priori the unknown number of clusters. We…

Machine Learning · Statistics 2020-11-13 Joshua Tobin , Mimi Zhang

A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on…

Data Structures and Algorithms · Computer Science 2021-10-27 Yuuki Takai , Atsushi Miyauchi , Masahiro Ikeda , Yuichi Yoshida

Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research. In thispaper, we provide a short proof that the adjacency spectral embedding can be used to obtain perfect clustering…

Machine Learning · Statistics 2015-01-19 Vince Lyzinski , Daniel Sussman , Minh Tang , Avanti Athreya , Carey Priebe

Graph clustering problems typically aim to partition the graph nodes such that two nodes belong to the same partition set if and only if they are similar. Correlation Clustering is a graph clustering formulation which: (1) takes as input a…

Social and Information Networks · Computer Science 2021-10-19 Jimit Majmudar , Stephen Vavasis

Two important optimization problems in the analysis of geometric data sets are clustering and sketching. Here, clustering refers to the problem of partitioning some input metric measure space (mm-space) into k clusters, minimizing some…

Computational Geometry · Computer Science 2018-10-19 Facundo Mémoli , Anastasios Sidiropoulos , Kritika Singhal

We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem…

Machine Learning · Computer Science 2021-03-31 Mireille El Gheche , Pascal Frossard

Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or…

Social and Information Networks · Computer Science 2023-07-20 Yu Tian , Zachary Lubberts , Melanie Weber