A tutorial on spectral clustering

@article{Luxburg2007ATO,
  title={A tutorial on spectral clustering},
  author={Ulrike von Luxburg},
  journal={Statistics and Computing},
  year={2007},
  volume={17},
  pages={395-416}
}
  • U. V. Luxburg
  • Published 1 November 2007
  • Computer Science
  • Statistics and Computing
Abstract In recent years, spectral clustering has become one of the most popular modern clustering algorithms. [] Key Method We describe different graph Laplacians and their basic properties, present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed.
The latest research progress on spectral clustering
TLDR
The basic concepts of graph theory are introduced and main matrix representations of the graph are reviewed, then the objective functions of typical graph cut methods are compared, and the nature of spectral clustering algorithm is explored.
Research on Spectral Clustering
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This paper describes different graph partition criteria, the definition of spectral clustering, and clustering steps, etc, and some improvements are introduced briefly in order to solve the disadvantage of spectral clusters.
A Note on Spectral Clustering Method Based on Normalized Cut Criterion
TLDR
A note is given on why the first k eigenvectors in the algorithm are chosen and the conditions for indicator vectors under which the clustering problem could lead to the problem of minimizing the objective function of the spectral clustering method based on normalized cut criterion.
An application of spectral clustering approach to detect communities in data modeled by graphs
TLDR
An application of spectral clustering to detect communities in data from real world after modeling those data by graphs and a comparison between the obtained results using the unnormalized and the normalized algorithms are presented.
A randomized algorithm for spectral clustering
TLDR
A bound for choosing a correct number of eigenvectors in a randomized spectral algorithm able to find a clustering solution is shown and the efficacy of the algorithm is shown with experiments on real world graphs.
Spectral Clustering on a Budget
TLDR
This paper focuses on the problem of performing spectral clustering under a budget constraint, where there is a limit on the number of entries which can be queried from the similarity matrix.
Partitioning Well-Clustered Graphs: Spectral Clustering Works!
TLDR
It is shown that spectral clustering gives a good approximation of the optimal clustering of graphs generated from stochastic models and a nearly linear time algorithm for partitioning well-clustered graphs based on computing a matrix exponential and approximate nearest neighbor data structures.
Spectral Clustering Survey HU , Pili
TLDR
This article aims at providing systematic ways to explore new spectral clustering algorithms through the analysis of a bunch of algorithms, and gives several unifying views of Spectral Embedding Technique: graph framework, kernel framework, trace maximization.
Principal coordinate clustering
This paper introduces a clustering algorithm, called principal coordinate clustering. It takes in a similarity matrix SW of a data matrix W and computes the singular value decomposition of SW to
A NEW SPECTRAL CLUSTERING APPROACH TO DETECTING COMMUNITIES IN GRAPHS
TLDR
This paper presents an approach for the detection of communities from graphs with Spectral Clustering, and used igraph package in language R for simulation and implementation.
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