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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

Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means…

Machine Learning · Computer Science 2017-11-15 Zhao Kang , Chong Peng , Qiang Cheng , Zenglin Xu

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

The performance of spectral clustering heavily relies on the quality of affinity matrix. A variety of affinity-matrix-construction (AMC) methods have been proposed but they have hyperparameters to determine beforehand, which requires strong…

Machine Learning · Computer Science 2023-02-07 Jicong Fan , Yiheng Tu , Zhao Zhang , Mingbo Zhao , Haijun Zhang

Spectral clustering is a leading and popular technique in unsupervised data analysis. Two of its major limitations are scalability and generalization of the spectral embedding (i.e., out-of-sample-extension). In this paper we introduce a…

Machine Learning · Statistics 2024-11-06 Uri Shaham , Kelly Stanton , Henry Li , Boaz Nadler , Ronen Basri , Yuval Kluger

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 popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter,…

Machine Learning · Statistics 2019-11-12 David Hofmeyr

In this paper we study variants of the widely used spectral clustering that partitions a graph into k clusters by (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and…

Data Structures and Algorithms · Computer Science 2017-02-01 Richard Peng , He Sun , Luca Zanetti

Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…

Machine Learning · Statistics 2013-09-18 Tai Qin , Karl Rohe

Spectral clustering is a powerful technique for clustering high-dimensional data, utilizing graph-based representations to detect complex, non-linear structures and non-convex clusters. The construction of a similarity graph is essential…

Machine Learning · Computer Science 2025-01-27 Kamal Berahmand , Farid Saberi-Movahed , Razieh Sheikhpour , Yuefeng Li , Mahdi Jalili

The two-step spectral clustering method, which consists of the Laplacian eigenmap and a rounding step, is a widely used method for graph partitioning. It can be seen as a natural relaxation to the NP-hard minimum ratio cut problem. In this…

Machine Learning · Statistics 2020-07-14 March Boedihardjo , Shaofeng Deng , Thomas Strohmer

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

Graph clustering aims at discovering a natural grouping of the nodes such that similar nodes are assigned to a common cluster. Many different algorithms have been proposed in the literature: for simple graphs, for graphs with attributes…

Machine Learning · Computer Science 2023-11-06 Ylli Sadikaj , Yllka Velaj , Sahar Behzadi , Claudia Plant

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

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

We revisit the theoretical performances of Spectral Clustering, a classical algorithm for graph partitioning that relies on the eigenvectors of a matrix representation of the graph. Informally, we show that Spectral Clustering works well as…

Machine Learning · Computer Science 2025-12-01 George Tyler , Luca Zanetti

Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…

Machine Learning · Computer Science 2022-09-27 Shubham Gupta , Ambedkar Dukkipati

We study the connections between spectral clustering and the problems of maximum margin clustering, and estimation of the components of level sets of a density function. Specifically, we obtain bounds on the eigenvectors of graph Laplacian…

Machine Learning · Statistics 2018-12-18 David P. Hofmeyr

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

We consider the problem of spectral clustering under group fairness constraints, where samples from each sensitive group are approximately proportionally represented in each cluster. Traditional fair spectral clustering (FSC) methods…

Machine Learning · Computer Science 2023-11-27 Xiang Zhang , Qiao Wang