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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

In this paper we generalise the results on eigenvalues and eigenvectors of unnormalized (combinatorial) Laplacian of two-dimensional grid presented by Edwards:2013 first to a grid graph of any dimension, and second also to other types of…

Classical Analysis and ODEs · Mathematics 2019-09-02 Mieczysław A. Kłopotek

In this work we study statistical properties of graph-based algorithms for multi-manifold clustering (MMC). In MMC the goal is to retrieve the multi-manifold structure underlying a given Euclidean data set when this one is assumed to be…

Machine Learning · Computer Science 2022-11-14 Nicolas Garcia Trillos , Pengfei He , Chenghui Li

Semi-supervised learning is highly useful in common scenarios where labeled data is scarce but unlabeled data is abundant. The graph (or nonlocal) Laplacian is a fundamental smoothing operator for solving various learning tasks. For…

Computer Vision and Pattern Recognition · Computer Science 2023-04-20 Or Streicher , Guy Gilboa

This paper introduces a graph Laplacian regularization in the hyperspectral unmixing formulation. The proposed regularization relies upon the construction of a graph representation of the hyperspectral image. Each node in the graph…

Computer Vision and Pattern Recognition · Computer Science 2014-10-15 Rita Ammanouil , André Ferrari , Cédric Richard

Graph-based multi-view clustering has become an active topic due to the efficiency in characterizing both the complex structure and relationship between multimedia data. However, existing methods have the following shortcomings: (1) They…

Computer Vision and Pattern Recognition · Computer Science 2021-08-17 Tianyu Jiang , Quanxue Gao , Xinbo Gao

We propose a Classification Via Clustering (CVC) algorithm which enables existing clustering methods to be efficiently employed in classification problems. In CVC, training and test data are co-clustered and class-cluster distributions are…

Computer Vision and Pattern Recognition · Computer Science 2014-09-29 Arif Mahmood , Ajmal S. Mian

The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used for spectral clustering and community detection. However, in real-life applications the number of clusters or…

Social and Information Networks · Computer Science 2018-01-24 Pin-Yu Chen , Baichuan Zhang , Mohammad Al Hasan , Alfred O. Hero

We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…

Methodology · Statistics 2015-09-28 Sayantan Banerjee , Rehan Akbani , Veerabhadran Baladandayuthapani

Local graph clustering and the closely related seed set expansion problem are primitives on graphs that are central to a wide range of analytic and learning tasks such as local clustering, community detection, nodes ranking and feature…

Machine Learning · Computer Science 2020-07-21 Kimon Fountoulakis , Di Wang , Shenghao Yang

Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…

Physics and Society · Physics 2025-01-31 James Martin , Tim Rogers , Luca Zanetti

Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…

Data Structures and Algorithms · Computer Science 2021-06-17 Vincent Cohen-Addad , Silvio Lattanzi , Slobodan Mitrović , Ashkan Norouzi-Fard , Nikos Parotsidis , Jakub Tarnawski

This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. Under a generalised random dot product graph, the embedding provides uniformly…

Methodology · Statistics 2021-05-05 Alexander Modell , Patrick Rubin-Delanchy

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

We present a new algorithm for spectral clustering based on a column-pivoted QR factorization that may be directly used for cluster assignment or to provide an initial guess for k-means. Our algorithm is simple to implement, direct, and…

Numerical Analysis · Mathematics 2017-04-18 Anil Damle , Victor Minden , Lexing Ying

A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…

Machine Learning · Computer Science 2024-10-07 Chakib Fettal , Lazhar Labiod , Mohamed Nadif

We propose a Greedy strategy to solve the problem of Graph Cut, called GGC. It starts from the state where each data sample is regarded as a cluster and dynamically merges the two clusters which reduces the value of the global objective…

Machine Learning · Computer Science 2024-12-31 Feiping Nie , Shenfei Pei , Zengwei Zheng , Rong Wang , Xuelong Li

Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of…

Statistics Theory · Mathematics 2008-12-18 Ulrike von Luxburg , Mikhail Belkin , Olivier Bousquet

Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is…

Machine Learning · Statistics 2020-04-09 Camille Champion , Blazère Mélanie , Burcelin Rémy , Loubes Jean-Michel , Risser Laurent

Dynamical Systems (DS) are fundamental to the modeling and understanding time evolving phenomena, and have application in physics, biology and control. As determining an analytical description of the dynamics is often difficult, data-driven…

Machine Learning · Computer Science 2022-11-23 Bernardo Fichera , Aude Billard