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Clustering is a fundamental task for analyzing unlabeled data based solely on its underlying distribution. Spectral clustering is a clustering method that represents a dataset as a graph and uses the relationships between data points.…

Quantum Physics · Physics 2025-04-01 Hyeong-Gyu Kim , Siheon Park , June-Koo Kevin Rhee

Spectral clustering is one of the most popular clustering methods for finding clusters in a graph, which has found many applications in data mining. However, the input graph in those applications may have many missing edges due to error in…

Data Structures and Algorithms · Computer Science 2020-06-09 Pan Peng , Yuichi Yoshida

Spectral clustering is discussed from many perspectives, by extending it to rectangular arrays and discrepancy minimization too. Near optimal clusters are obtained with singular value decomposition and with the weighted $k$-means algorithm.…

Combinatorics · Mathematics 2022-01-06 Marianna Bolla , Vilas Winstein , Tao You , Frank Seidl , Fatma Abdelkhalek

Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices. We expand upon recent results in spectral analysis for…

Statistics Theory · Mathematics 2022-03-23 Denis Gaidashev , Ralf Pihlström , Martin Ryner

Large-scale multi-layer networks with large numbers of nodes, edges, and layers arise across various domains, which poses a great computational challenge for the downstream analysis. In this paper, we develop an efficient randomized…

Computation · Statistics 2025-01-10 Wenqing Su , Xiao Guo , Xiangyu Chang , Ying Yang

This article considers spectral community detection in the regime of sparse networks with heterogeneous degree distributions, for which we devise an algorithm to efficiently retrieve communities. Specifically, we demonstrate that a…

Machine Learning · Statistics 2021-10-12 Lorenzo Dall'Amico , Romain Couillet , Nicolas Tremblay

We consider spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or…

Statistics Theory · Mathematics 2018-12-27 Zhixin Zhou , Arash A. Amini

Graph-based clustering methods like spectral clustering and SpectralNet are very efficient in detecting clusters of non-convex shapes. Unlike the popular $k$-means, graph-based clustering methods do not assume that each cluster has a single…

Machine Learning · Computer Science 2023-02-28 Mashaan Alshammari , John Stavrakakis , Masahiro Takatsuka

This article proposes a first analysis of kernel spectral clustering methods in the regime where the dimension $p$ of the data vectors to be clustered and their number $n$ grow large at the same rate. We demonstrate, under a $k$-class…

Statistics Theory · Mathematics 2016-04-22 Romain Couillet , Florent Benaych-Georges

Spectral clustering methods are widely used for detecting clusters in networks for community detection, while a small change on the graph Laplacian matrix could bring a dramatic improvement. In this paper, we propose a dual regularized…

Machine Learning · Statistics 2020-11-10 Huan Qing , Jingli Wang

Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral…

Social and Information Networks · Computer Science 2022-01-07 Hai Zhang , Xiao Guo , Xiangyu Chang

Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster.…

Machine Learning · Computer Science 2021-01-01 Filippo Maria Bianchi , Daniele Grattarola , Cesare Alippi

The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used in spectral clustering and community detection. However, in real-life applications the number of clusters or…

Machine Learning · Computer Science 2018-01-26 Pin-Yu Chen , Baichuan Zhang , Mohammad Al Hasan

Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…

Machine Learning · Statistics 2022-08-01 Elise van der Pol , Ian Gemp , Yoram Bachrach , Richard Everett

Spectral clustering is one of the most widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and…

Numerical Analysis · Mathematics 2010-11-05 Blake Hunter , Thomas Strohmer

Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale…

Machine Learning · Computer Science 2020-09-11 Hengrui Wang , Yubo Zhang , Mingzhi Chen , Tong Yang

Spectral clustering is a powerful method for finding structure in a dataset through the eigenvectors of a similarity matrix. It often outperforms traditional clustering algorithms such as $k$-means when the structure of the individual…

Numerical Analysis · Mathematics 2019-04-26 Paola Favati , Grazia Lotti , Ornella Menchi , Francesco Romani

We present a new algorithm for spectral clustering based on a column-pivoted QR factorization that may be directly used for cluster assignment or to provide an initial guess for k-means. Our algorithm is simple to implement, direct, and…

Numerical Analysis · Mathematics 2017-04-18 Anil Damle , Victor Minden , Lexing Ying

A basic problem in spectral clustering is the following. If a solution obtained from the spectral relaxation is close to an integral solution, is it possible to find this integral solution even though they might be in completely different…

Data Structures and Algorithms · Computer Science 2015-10-20 Ali Kemal Sinop

Graph clustering or community detection constitutes an important task for investigating the internal structure of graphs, with a plethora of applications in several domains. Traditional techniques for graph clustering, such as spectral…