A tutorial on spectral clustering

Authors:
Ulrike Luxburg
Affiliations:
Max Planck Institute for Biological Cybernetics, Tübingen, Germany 72076
Venue:
Statistics and Computing
Year:
2007

Citing 26
Cited 305

Partitioning sparse matrices with eigenvectors of graphs

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An improved spectral graph partitioning algorithm for mapping parallel computations

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A decentralized algorithm for spectral analysis

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Fast SDP Relaxations of Graph Cut Clustering, Transduction, and Other Combinatorial Problems

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Random-Walk Computation of Similarities between Nodes of a Graph with Application to Collaborative Recommendation

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Graph Laplacians and their Convergence on Random Neighborhood Graphs

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Drawing graphs by eigenvectors: theory and practice

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Uniform convergence of adaptive graph-based regularization

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Euclidean distances, soft and spectral clustering on weighted graphs

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Operator Norm Convergence of Spectral Clustering on Level Sets

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Spectral clustering with fuzzy similarity measure

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ACM Transactions on Graphics (TOG)
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Class consistent k-means: Application to face and action recognition

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Optimal and hierarchical clustering of large-scale hybrid networks for scientific mapping

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Active spectral clustering via iterative uncertainty reduction

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SIAM Journal on Scientific Computing
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A VNS heuristic for escaping local extrema entrapment in normalized cut clustering

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Semi-supervised clustering with discriminative random fields

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Applied Soft Computing
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Hierarchical kernel spectral clustering

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Kernelized temporal cut for online temporal segmentation and recognition

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Group-Wise consistent parcellation of gyri via adaptive multi-view spectral clustering of fiber shapes

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Hypergraph learning with hyperedge expansion

ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
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KI'12 Proceedings of the 35th Annual German conference on Advances in Artificial Intelligence
Self-Organizing map and tree topology for graph summarization

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MSM'11 Proceedings of the 2011 international conference on Modeling and Mining Ubiquitous Social Media
Spectral clustering based on k-nearest neighbor graph

CISIM'12 Proceedings of the 11th IFIP TC 8 international conference on Computer Information Systems and Industrial Management
On spectral partitioning of co-authorship networks

CISIM'12 Proceedings of the 11th IFIP TC 8 international conference on Computer Information Systems and Industrial Management
Delineation of liver tumors from CT scans using spectral clustering with out-of-sample extension and multi-windowing

MICCAI'12 Proceedings of the 4th international conference on Abdominal Imaging: computational and clinical applications
On-line spectral learning in exploring 3d large scale geo-referred scenes

EuroMed'12 Proceedings of the 4th international conference on Progress in Cultural Heritage Preservation
Modified divergences for Gaussian densities

SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Nonlinear Multilayered Representation of Graph-Signals

Journal of Mathematical Imaging and Vision
Advanced graph mining for community evaluation in social networks and the web

Proceedings of the sixth ACM international conference on Web search and data mining
Segmentation of temporal mesh sequences into rigidly moving components

Graphical Models
CIUCEU: Multi-Agent-Based Simulation of University Email Communities

International Journal of Agent Technologies and Systems
Content-Based Keyframe Clustering Using Near Duplicate Keyframe Identification

International Journal of Multimedia Data Engineering & Management
Transforming graph data for statistical relational learning

Journal of Artificial Intelligence Research
Multi-view action recognition based on action volumes, fuzzy distances and cluster discriminant analysis

Signal Processing
Interconnection of asynchronous Boolean networks, asymptotic and transient dynamics

Automatica (Journal of IFAC)
Combining Relations and Text in Scientific Network Clustering

ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
Using Field of Research Codes to Discover Research Groups from Co-authorship Networks

ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
Global Similarity in Social Networks with Typed Edges

ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
Document Re-ranking Using Partial Social Tagging

WI-IAT '12 Proceedings of the The 2012 IEEE/WIC/ACM International Joint Conferences on Web Intelligence and Intelligent Agent Technology - Volume 01
Toward finding hidden communities based on user profile

Journal of Intelligent Information Systems
Random walk distances in data clustering and applications

Advances in Data Analysis and Classification
Regional appearance modeling based on the clustering of intensity profiles

Computer Vision and Image Understanding
Think globally, act locally: on the reshaping of information landscapes

Proceedings of the 12th international conference on Information processing in sensor networks
Automatic virtual machine clustering based on bhattacharyya distance for multi-cloud systems

Proceedings of the 2013 international workshop on Multi-cloud applications and federated clouds
Constrained spectral embedding for K-way data clustering

Pattern Recognition Letters
Graph-Based approaches to clustering network-constrained trajectory data

NFMCP'12 Proceedings of the First international conference on New Frontiers in Mining Complex Patterns
A genetic graph-based clustering approach to biomedical summarization

Proceedings of the 3rd International Conference on Web Intelligence, Mining and Semantics
Efficient discriminative learning of class hierarchy for many class prediction

ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part I
Multiple feature fusion based on co-training approach and time regularization for place classification in wearable video

Advances in Multimedia
A spectral clustering approach to application-specific network-on-chip synthesis

Proceedings of the Conference on Design, Automation and Test in Europe
Spectral analysis of communication networks using Dirichlet eigenvalues

Proceedings of the 22nd international conference on World Wide Web
Spectral embedding for dynamic social networks

Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
Solving the missing node problem using structure and attribute information

Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
The influence of feedback with different opinions on continued user participation in online newsgroups

Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
Machine learning for interactive systems and robots: a brief introduction

Proceedings of the 2nd Workshop on Machine Learning for Interactive Systems: Bridging the Gap Between Perception, Action and Communication
The community structure of a multidimensional network of news clips

International Journal of Web Based Communities
Robust clustering for social annotated images

Proceedings of the Fifth International Conference on Internet Multimedia Computing and Service
PathSelClus: Integrating Meta-Path Selection with User-Guided Object Clustering in Heterogeneous Information Networks

ACM Transactions on Knowledge Discovery from Data (TKDD) - Special Issue on ACM SIGKDD 2012
Parallel reduction to hessenberg form with algorithm-based fault tolerance

SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Data clustering using controlled consensus in complex networks

Neurocomputing
Image retrieval based on augmented relational graph representation

Applied Intelligence
A Framework for Identifying Affinity Classes of Inorganic Materials Binding Peptide Sequences

Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
Biomedical time series clustering based on non-negative sparse coding and probabilistic topic model

Computer Methods and Programs in Biomedicine
Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification

Advances in Data Analysis and Classification
Semantic discovery from web comparison queries

Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
Dynamic group-finding in public bus networks

Proceedings of the 2nd ACM workshop on High performance mobile opportunistic systems
A non-parametric unsupervised approach for content based image retrieval and clustering

Proceedings of the 4th ACM/IEEE international workshop on Analysis and retrieval of tracked events and motion in imagery stream
Combining co-clustering with noise detection for theme-based summarization

ACM Transactions on Speech and Language Processing (TSLP)
SMI 2013: Grouping real functions defined on 3D surfaces

Computers and Graphics
SMI 2013: Unsupervised co-segmentation of 3D shapes via affinity aggregation spectral clustering

Computers and Graphics
Clustering and outlier detection using isoperimetric number of trees

Pattern Recognition
Outsourcing location selection with SODA: a requirements based decision support methodology and tool

CAiSE'13 Proceedings of the 25th international conference on Advanced Information Systems Engineering
Construction of multi-scale common brain networks based on DICCCOL

IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
An overlapped community partition algorithm based on line graph

WAIM'13 Proceedings of the 14th international conference on Web-Age Information Management
Finding critical blocks of information diffusion in social networks

WAIM'13 Proceedings of the 14th international conference on Web-Age Information Management
Information theoretic pairwise clustering

SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
Multi-task averaging via task clustering

SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
Active learning for protein function prediction in protein-protein interaction networks

PRIB'13 Proceedings of the 8th IAPR international conference on Pattern Recognition in Bioinformatics
Mesh saliency via spectral processing

ACM Transactions on Graphics (TOG)
On the statistical detection of clusters in undirected networks

Computational Statistics & Data Analysis
QUAC: Quick unsupervised anisotropic clustering

Pattern Recognition
Non-negative and sparse spectral clustering

Pattern Recognition
Integrating tracking with fine object segmentation

Image and Vision Computing
Persistence-Based Clustering in Riemannian Manifolds

Journal of the ACM (JACM)
Towards effective clustering techniques for the analysis of electric power grids

HiPCNA-PG '13 Proceedings of the 3rd International Workshop on High Performance Computing, Networking and Analytics for the Power Grid
A spectral clustering algorithm based on intuitionistic fuzzy information

Knowledge-Based Systems
Efficient kernel learning from side information using ADMM

IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Coupled attribute analysis on numerical data

IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Social trust prediction using heterogeneous networks

ACM Transactions on Knowledge Discovery from Data (TKDD)
Editor's Choice Article: Human activity recognition in videos using a single example

Image and Vision Computing
A spectral approach to detecting subtle anomalies in graphs

Journal of Intelligent Information Systems
Deflation-based power iteration clustering

Applied Intelligence
On constrained spectral clustering and its applications

Data Mining and Knowledge Discovery
Combining supervised and unsupervised models via unconstrained probabilistic embedding

Information Sciences: an International Journal
The learning system of collective behavior in students' social network

Computers and Electrical Engineering
Local information-based fast approximate spectral clustering

Pattern Recognition Letters
A non-parametric method to estimate the number of clusters

Computational Statistics & Data Analysis
Maximum volume clustering: a new discriminative clustering approach

The Journal of Machine Learning Research
Clustering in extreme learning machine feature space

Neurocomputing
Graph Partitioning by Correspondence Analysis and Taxicab Correspondence Analysis

Journal of Classification
PSG: a two-layer graph model for document summarization

Frontiers of Computer Science: Selected Publications from Chinese Universities
Summarizing high-level scene behavior

Machine Vision and Applications
Subspace clustering of high-dimensional data: a predictive approach

Data Mining and Knowledge Discovery
Efficient eigen-updating for spectral graph clustering

Neurocomputing
Adaptive evolutionary clustering

Data Mining and Knowledge Discovery
Sentiment analysis based on clustering: a framework in improving accuracy and recognizing neutral opinions

Applied Intelligence
A re-coloring approach for graph b-coloring based clustering

International Journal of Knowledge-based and Intelligent Engineering Systems
Rectifying the representation learned by Non-negative Matrix Factorization

International Journal of Knowledge-based and Intelligent Engineering Systems
Detecting network communities using regularized spectral clustering algorithm

Artificial Intelligence Review
Robust human action recognition scheme based on high-level feature fusion

Multimedia Tools and Applications
Spectral Log-Demons: Diffeomorphic Image Registration with Very Large Deformations

International Journal of Computer Vision

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Abstract

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 clustering algorithms such as the k-means algorithm. On the first glance spectral clustering appears slightly mysterious, and it is not obvious to see why it works at all and what it really does. The goal of this tutorial is to give some intuition on those questions. 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.