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Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach…

Machine Learning · Statistics 2017-06-13 Lionel Martin , Andreas Loukas , Pierre Vandergheynst

While spectral clustering algorithms for undirected graphs are well established and have been successfully applied to unsupervised machine learning problems ranging from image segmentation and genome sequencing to signal processing and…

Dynamical Systems · Mathematics 2022-11-23 Stefan Klus , Natasa Djurdjevac Conrad

As the most typical graph clustering method, spectral clustering is popular and attractive due to the remarkable performance, easy implementation, and strong adaptability. Classical spectral clustering measures the edge weights of graph…

Machine Learning · Computer Science 2023-12-08 Dehua Peng , Zhipeng Gui , Huayi Wu

Graph clustering is a fundamental task in network analysis where the goal is to detect sets of nodes that are well-connected to each other but sparsely connected to the rest of the graph. We present faster approximation algorithms for an…

Data Structures and Algorithms · Computer Science 2023-06-09 Vedangi Bengali , Nate Veldt

A basic fact in spectral graph theory is that the number of connected components in an undirected graph is equal to the multiplicity of the eigenvalue zero in the Laplacian matrix of the graph. In particular, the graph is disconnected if…

Metric Geometry · Mathematics 2014-11-24 James R. Lee , Shayan Oveis Gharan , Luca Trevisan

In this paper, we focus on graph learning from multi-view data of shared entities for spectral clustering. We can explain interactions between the entities in multi-view data using a multi-layer graph with a common vertex set, which…

Machine Learning · Computer Science 2021-03-04 Sravanthi Gurugubelli , Sundeep Prabhakar Chepuri

Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…

Computer Vision and Pattern Recognition · Computer Science 2024-06-10 Rahul Palnitkar , Jeova Farias Sales Rocha Neto

The implementation of a vast majority of machine learning (ML) algorithms boils down to solving a numerical optimization problem. In this context, Stochastic Gradient Descent (SGD) methods have long proven to provide good results, both in…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-10-06 Janis Keuper , Franz-Josef Pfreundt

We show how to efficiently solve a clustering problem that arises in a method to evaluate functions of matrices. The problem requires finding the connected components of a graph whose vertices are eigenvalues of a real or complex matrix and…

Computational Geometry · Computer Science 2020-03-27 Nir Goren , Dan Halperin , Sivan Toledo

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and…

Machine Learning · Statistics 2018-10-03 Daniel Korenblum

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

Large-scale L1-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. High-performance algorithms…

Machine Learning · Statistics 2012-12-19 Chad Scherrer , Ambuj Tewari , Mahantesh Halappanavar , David Haglin

Several fundamental tasks in data science rely on computing an extremal eigenspace of size $r \ll n$, where $n$ is the underlying problem dimension. For example, spectral clustering and PCA both require the computation of the leading…

Numerical Analysis · Mathematics 2019-09-04 Vasileios Charisopoulos , Austin R. Benson , Anil Damle

We propose a symmetric graph convolutional autoencoder which produces a low-dimensional latent representation from a graph. In contrast to the existing graph autoencoders with asymmetric decoder parts, the proposed autoencoder has a newly…

Machine Learning · Computer Science 2019-08-08 Jiwoong Park , Minsik Lee , Hyung Jin Chang , Kyuewang Lee , Jin Young Choi

What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics. Some solutions assume that auxiliary information on…

Information Retrieval · Computer Science 2021-06-14 Judith Hermanns , Anton Tsitsulin , Marina Munkhoeva , Alex Bronstein , Davide Mottin , Panagiotis Karras

Subspace clustering seeks to identify subspaces that segment a set of n data points into k (k<<n) groups, which has emerged as a powerful tool for analyzing data from various domains, especially images and videos. Recently, several studies…

Social and Information Networks · Computer Science 2024-11-19 Xiaoyang Lin , Renchi Yang , Haoran Zheng , Xiangyu Ke

Graph summarization via node grouping is a popular method to build concise graph representations by grouping nodes from the original graph into supernodes and encoding edges into superedges such that the loss of adjacency information is…

Social and Information Networks · Computer Science 2022-11-09 Arpit Merchant , Michael Mathioudakis , Yanhao Wang

Spectral clustering is a widely used algorithm to find clusters in networks. Several researchers have studied the stability of spectral clustering under local differential privacy with the additional assumption that the underlying networks…

Cryptography and Security · Computer Science 2025-05-15 Sayan Mukherjee , Vorapong Suppakitpaisarn

Contrastive learning has recently attracted plenty of attention in deep graph clustering for its promising performance. However, complicated data augmentations and time-consuming graph convolutional operation undermine the efficiency of…

Machine Learning · Computer Science 2022-06-28 Yue Liu , Xihong Yang , Sihang Zhou , Xinwang Liu

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