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Related papers: Eigenvalue-based Incremental Spectral Clustering

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The rich spectral information of the graph Laplacian has been instrumental in graph theory, machine learning, and graph signal processing for applications such as graph classification, clustering, or eigenmode analysis. Recently, the Hodge…

Algebraic Topology · Mathematics 2024-03-27 Vincent P. Grande , Michael T. Schaub

In many real-world applications, we have access to multiple views of the data, each of which characterizes the data from a distinct aspect. Several previous algorithms have demonstrated that one can achieve better clustering accuracy by…

Computer Vision and Pattern Recognition · Computer Science 2017-08-01 Tyng-Luh Liu

We use a cluster ensemble to determine the number of clusters, k, in a group of data. A consensus similarity matrix is formed from the ensemble using multiple algorithms and several values for k. A random walk is induced on the graph…

Machine Learning · Statistics 2014-08-06 Shaina Race , Carl Meyer , Kevin Valakuzhy

Spectral Clustering is a popular technique to split data points into groups, especially for complex datasets. The algorithms in the Spectral Clustering family typically consist of multiple separate stages (such as similarity matrix…

Machine Learning · Computer Science 2019-11-04 Yifei Wang , Rui Liu , Yong Chen , Hui Zhangs , Zhiwen Ye

An agglomerative clustering of random variables is proposed, where clusters of random variables sharing the maximum amount of multivariate mutual information are merged successively to form larger clusters. Compared to the previous…

Information Theory · Computer Science 2017-02-27 Chung Chan , Ali Al-Bashabsheh , Qiaoqiao Zhou

Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of…

Machine Learning · Statistics 2011-12-14 Karl Rohe , Sourav Chatterjee , Bin Yu

An important form of prior information in clustering comes in form of cannot-link and must-link constraints. We present a generalization of the popular spectral clustering technique which integrates such constraints. Motivated by the…

Machine Learning · Statistics 2015-05-26 Syama Sundar Rangapuram , Matthias Hein

Spectral clustering algorithms typically require a priori selection of input parameters such as the number of clusters, a scaling parameter for the affinity measure, or ranges of these values for parameter tuning. Despite efforts for…

Machine Learning · Computer Science 2019-03-20 Milad Afzalan , Farrokh Jazizadeh

In spectral clustering and spectral image segmentation, the data is partioned starting from a given matrix of pairwise similarities S. the matrix S is constructed by hand, or learned on a separate training set. In this paper we show how to…

Machine Learning · Computer Science 2012-07-09 Susan Shortreed , Marina Meila

Spectral clustering methods are known for their ability to represent clusters of diverse shapes, densities etc. However, results of such algorithms, when applied e.g. to text documents, are hard to explain to the user, especially due to…

Machine Learning · Computer Science 2023-08-02 Bartłomiej Starosta , Mieczysław A. Kłopotek , Sławomir T. Wierzchoń

Following Hartigan, a cluster is defined as a connected component of the t-level set of the underlying density, i.e., the set of points for which the density is greater than t. A clustering algorithm which combines a density estimate with…

Machine Learning · Statistics 2010-02-12 Bruno Pelletier , Pierre Pudlo

Despite tremendous advancements in Artificial Intelligence, learning from large sets of data in an unsupervised manner remains a significant challenge. Classical clustering algorithms often fail to discover complex dependencies in large…

Machine Learning · Computer Science 2023-07-18 Adam Piróg , Halina Kwaśnicka

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

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 uses a graph Laplacian spectral embedding to enhance the cluster structure of some data sets. When the embedding is one dimensional, it can be used to sort the items (spectral ordering). A number of empirical results…

Data Structures and Algorithms · Computer Science 2018-07-20 Antoine Recanati , Thomas Kerdreux , Alexandre d'Aspremont

This study presents a novel approach utilizing cluster means to address the non-differentiability issue arising from multiple eigenvalues in eigenfrequency and bandgap optimization. By constructing symmetric functions of repeated…

Computational Engineering, Finance, and Science · Computer Science 2025-01-28 Shiyao Sun , Kapil Khandelwal

While orthogonalization exists in current dimensionality reduction methods in spectral clustering on undirected graphs, it does not scale in parallel computing environments. We propose four orthogonalization-free methods for spectral…

Signal Processing · Electrical Eng. & Systems 2024-11-05 Qiyuan Pang , Haizhao Yang

Traditional image clustering methods take a two-step approach, feature learning and clustering, sequentially. However, recent research results demonstrated that combining the separated phases in a unified framework and training them jointly…

Computer Vision and Pattern Recognition · Computer Science 2017-03-24 Fengfu Li , Hong Qiao , Bo Zhang , Xuanyang Xi

In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional…

Data Structures and Algorithms · Computer Science 2007-11-02 Ulrike von Luxburg

Spectral clustering uses the global information embedded in eigenvectors of an inter-item similarity matrix to correctly identify clusters of irregular shape, an ability lacking in commonly used approaches such as k-means and agglomerative…

Data Analysis, Statistics and Probability · Physics 2010-01-18 Brian White , David Shalloway