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Related papers: Robust spectral clustering with rank statistics

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The problem of clustering noisy and incompletely observed high-dimensional data points into a union of low-dimensional subspaces and a set of outliers is considered. The number of subspaces, their dimensions, and their orientations are…

Machine Learning · Statistics 2015-08-24 Reinhard Heckel , Helmut Bölcskei

Among community detection methods, spectral clustering enjoys two desirable properties: computational efficiency and theoretical guarantees of consistency. Most studies of spectral clustering consider only the edges of a network as input to…

Machine Learning · Statistics 2022-05-18 Jonathan Hehir , Xiaoyue Niu , Aleksandra Slavkovic

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

Motivated by a neuroscience application we study the problem of statistical estimation of a high-dimensional covariance matrix with a block structure. The block model embeds a structural assumption: the population of items (neurons) can be…

Methodology · Statistics 2025-03-03 Yunran Chen , Surya T Tokdar , Jennifer M Groh

Despite the ubiquity of kernel-based clustering, surprisingly few statistical guarantees exist beyond settings that consider strong structural assumptions on the data generation process. In this work, we take a step towards bridging this…

Machine Learning · Computer Science 2021-10-19 Leena Chennuru Vankadara , Sebastian Bordt , Ulrike von Luxburg , Debarghya Ghoshdastidar

We consider the community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), a general model of random networks with community structure and higher-order interactions. When the…

Statistics Theory · Mathematics 2024-12-11 Ioana Dumitriu , Haixiao Wang , Yizhe Zhu

Classical multidimensional scaling is an important dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing the quality of…

Statistics Theory · Mathematics 2020-07-09 Anna Little , Yuying Xie , Qiang Sun

Spectral clustering is a popular method for effectively clustering nonlinearly separable data. However, computational limitations, memory requirements, and the inability to perform incremental learning challenge its widespread application.…

Machine Learning · Computer Science 2023-11-15 Jo-Chun Chen , Hung-Hsuan Chen

Spectral clustering is a popular and effective algorithm designed to find $k$ clusters in a graph $G$. In the classical spectral clustering algorithm, the vertices of $G$ are embedded into $\mathbb{R}^k$ using $k$ eigenvectors of the graph…

Data Structures and Algorithms · Computer Science 2023-10-18 Peter Macgregor

We propose a novel model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix that models the…

Systems and Control · Electrical Eng. & Systems 2022-10-04 Hancheng Min , Enrique Mallada

Spectral embedding of network adjacency matrices often produces node representations living approximately around low-dimensional submanifold structures. In particular, hidden substructure is expected to arise when the graph is generated…

Machine Learning · Statistics 2022-06-27 Francesco Sanna Passino , Nicholas A. Heard

Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…

Machine Learning · Computer Science 2019-01-30 Nicolas Tremblay , Andreas Loukas

Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of…

Machine Learning · Statistics 2016-09-12 Pan Zhang

We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The subspace clustering problem has…

Computer Vision and Pattern Recognition · Computer Science 2013-08-02 Qiang Qiu , Guillermo Sapiro

In this paper, we propose a low-rank representation with symmetric constraint (LRRSC) method for robust subspace clustering. Given a collection of data points approximately drawn from multiple subspaces, the proposed technique can…

Computer Vision and Pattern Recognition · Computer Science 2017-05-16 Jie Chen , Hua Mao , Yongsheng Sang , Zhang Yi

We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix…

Systems and Control · Electrical Eng. & Systems 2023-05-15 Hancheng Min , Enrique Mallada

The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the…

Machine Learning · Computer Science 2020-07-27 Benjamin W. Priest , Alec Dunton , Geoffrey Sanders

We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…

Computer Vision and Pattern Recognition · Computer Science 2017-09-06 João Carvalho , Manuel Marques , João P. Costeira

We study graph clustering in the Stochastic Block Model (SBM) in the presence of both large clusters and small, unrecoverable clusters. Previous convex relaxation approaches achieving exact recovery do not allow any small clusters of size…

Machine Learning · Computer Science 2025-02-25 Matthew Zurek , Yudong Chen

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