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Related papers: Consistency of spectral clustering

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The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…

Machine Learning · Computer Science 2010-05-31 Daniil Ryabko

The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It…

Machine Learning · Computer Science 2021-03-16 Konstantin Avrachenkov , Andrei Bobu , Maximilien Dreveton

We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden…

Statistics Theory · Mathematics 2014-12-31 Jing Lei , Alessandro Rinaldo

Spectral clustering is one of the most important algorithms in data mining and machine intelligence; however, its computational complexity limits its application to truly large scale data analysis. The computational bottleneck in spectral…

Machine Learning · Computer Science 2015-05-13 Christos Boutsidis , Alex Gittens , Prabhanjan Kambadur

Our previous experiments demonstrated that subsets collections of (short) documents (with several hundred entries) share a common normalized in some way eigenvalue spectrum of combinatorial Laplacian. Based on this insight, we propose a…

Machine Learning · Computer Science 2023-08-23 Mieczysław A. Kłopotek , Bartłmiej Starosta , Sławomir T. Wierzchoń

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

This paper establishes the consistency of spectral approaches to data clustering. We consider clustering of point clouds obtained as samples of a ground-truth measure. A graph representing the point cloud is obtained by assigning weights to…

Statistics Theory · Mathematics 2015-08-11 Nicolás García Trillos , Dejan Slepčev

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 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 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 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

Community detection in network analysis is an attractive research area recently. Here, under the degree-corrected mixed membership (DCMM) model, we propose an efficient approach called mixed regularized spectral clustering (Mixed-RSC for…

Social and Information Networks · Computer Science 2021-08-30 Huan Qing , Jingli Wang

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

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

Constrained clustering has been well-studied for algorithms such as $K$-means and hierarchical clustering. However, how to satisfy many constraints in these algorithmic settings has been shown to be intractable. One alternative to encode…

Machine Learning · Computer Science 2012-09-24 Xiang Wang , Buyue Qian , Ian Davidson

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 one of the most popular clustering methods. However, the high computational cost due to the involved eigen-decomposition procedure can immediately hinder its applications in large-scale tasks. In this paper we use…

Machine Learning · Computer Science 2023-01-24 Yongyu Wang

Spectral embedding is a popular technique for the representation of graph data. Several regularization techniques have been proposed to improve the quality of the embedding with respect to downstream tasks like clustering. In this paper, we…

Machine Learning · Computer Science 2019-12-24 Nathan de Lara , Thomas Bonald

Spectral clustering is a novel clustering method which can detect complex shapes of data clusters. However, it requires the eigen decomposition of the graph Laplacian matrix, which is proportion to $O(n^3)$ and thus is not suitable for…

Machine Learning · Computer Science 2013-07-02 Nguyen Lu Dang Khoa , Sanjay Chawla

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…