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In a graph bisection problem, we are given a graph $G$ with two equally-sized unlabeled communities, and the goal is to recover the vertices in these communities. A popular heuristic, known as spectral clustering, is to output an estimated…

This paper focuses on obtaining clustering information about a distribution from its i.i.d. samples. We develop theoretical results to understand and use clustering information contained in the eigenvectors of data adjacency matrices based…

Machine Learning · Statistics 2009-11-20 Tao Shi , Mikhail Belkin , Bin Yu

Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition…

Machine Learning · Statistics 2022-08-10 Francesco Sanna Passino , Nicholas A. Heard , Patrick Rubin-Delanchy

Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to…

Physics and Society · Physics 2014-02-25 Fabrizio De Vico Fallani , Vincenzo Nicosia , Vito Latora , Mario Chavez

Network clustering reveals the organization of a network or corresponding complex system with elements represented as vertices and interactions as edges in a (directed, weighted) graph. Although the notion of clustering can be somewhat…

Machine Learning · Statistics 2017-11-15 Yongjin Park , Joel S. Bader

Spectral clustering is widely used in practice due to its flexibility, computational efficiency, and well-understood theoretical performance guarantees. Recently, spectral clustering has been studied to find balanced clusters under…

Machine Learning · Statistics 2022-03-07 Shubham Gupta , Ambedkar Dukkipati

The stochastic block model is a natural model for studying community detection in random networks. Its clustering properties have been extensively studied in the statistics, physics and computer science literature. Recently this area has…

Probability · Mathematics 2020-05-05 Gerandy Brito , Ioana Dumitriu , Shirshendu Ganguly , Christopher Hoffman , Linh V. Tran

In this paper we prove the strong consistency of several methods based on the spectral clustering techniques that are widely used to study the community detection problem in stochastic block models (SBMs). We show that under some weak…

Methodology · Statistics 2019-05-16 Liangjun Su , Wuyi Wang , Yichong Zhang

Spectral clustering is a broad class of clustering procedures in which an intractable combinatorial optimization formulation of clustering is "relaxed" into a tractable eigenvector problem, and in which the relaxed solution is subsequently…

Methodology · Statistics 2011-02-21 Zhihua Zhang , Michael I. Jordan

We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the…

Discrete Mathematics · Computer Science 2015-03-13 Tuhin Sahai , Alberto Speranzon , Andrzej Banaszuk

We study the Personalized PageRank (PPR) algorithm, a local spectral method for clustering, which extracts clusters using locally-biased random walks around a given seed node. In contrast to previous work, we adopt a classical statistical…

Statistics Theory · Mathematics 2021-12-24 Alden Green , Sivaraman Balakrishnan , Ryan J. Tibshirani

Spectral clustering is a well-known technique which identifies $k$ clusters in an undirected graph with weight matrix $W\in\mathbb{R}^{n\times n}$ by exploiting its graph Laplacian $L(W)$, whose eigenvalues $0=\lambda_1\leq \lambda_2 \leq…

Numerical Analysis · Mathematics 2023-06-08 Nicola Guglielmi , Stefano Sicilia

Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…

Machine Learning · Computer Science 2016-03-17 Shahzad Bhatti , Carolyn Beck , Angelia Nedic

Spectral clustering uses a graph Laplacian spectral embedding to enhance the cluster structure of some data sets. When the embedding is one dimensional, it can be used to sort the items (spectral ordering). A number of empirical results…

Data Structures and Algorithms · Computer Science 2018-07-20 Antoine Recanati , Thomas Kerdreux , Alexandre d'Aspremont

Spectral clustering is one of the most popular unsupervised machine learning methods. Constructing similarity matrix is crucial to this type of method. In most existing works, the similarity matrix is computed once for all or is updated…

Machine Learning · Computer Science 2023-06-30 Yongyan Guo , Gang Wu

One of the most widely used techniques for data clustering is agglomerative clustering. Such algorithms have been long used across many different fields ranging from computational biology to social sciences to computer vision in part…

Machine Learning · Computer Science 2014-07-15 Maria-Florina Balcan , Yingyu Liang , Pramod Gupta

Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…

Machine Learning · Statistics 2021-10-26 Yuxin Chen , Yuejie Chi , Jianqing Fan , Cong Ma

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

This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…

Social and Information Networks · Computer Science 2022-12-06 Mostafa Rahmani , Andre Beckus , Adel Karimian , George Atia

Spectral clustering has been widely used for community detection in network sciences. While its empirical successes are well-documented, a clear theoretical understanding, particularly for sparse networks where degrees are much smaller than…

Statistics Theory · Mathematics 2024-05-13 Anderson Ye Zhang