Spectra, Euclidean representations and clusterings of hypergraphs
Discrete Mathematics
Spectra of regular graphs and hypergraphs and orthogonal polynomials
European Journal of Combinatorics
Spectral partitioning with multiple eigenvectors
Discrete Applied Mathematics - Special volume on VLSI
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Clustering Categorical Data: An Approach Based on Dynamical Systems
VLDB '98 Proceedings of the 24rd International Conference on Very Large Data Bases
Semi-Supervised Learning on Riemannian Manifolds
Machine Learning
A Tensor Decomposition for Geometric Grouping and Segmentation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Non-negative tensor factorization with applications to statistics and computer vision
ICML '05 Proceedings of the 22nd international conference on Machine learning
Multi-way clustering using super-symmetric non-negative tensor factorization
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Regularization on discrete spaces
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
Multilevel spectral hypergraph partitioning with arbitrary vertex sizes
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
RSS: A framework enabling ranked search on the semantic web
Information Processing and Management: an International Journal
Hypergraph spectral learning for multi-label classification
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Modeling video hyperlinks with hypergraph for web video reranking
MM '08 Proceedings of the 16th ACM international conference on Multimedia
Spectral Embedding of Feature Hypergraphs
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Spectral Curvature Clustering (SCC)
International Journal of Computer Vision
A least squares formulation for a class of generalized eigenvalue problems in machine learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Interactive image segmentation using probabilistic hypergraphs
Pattern Recognition
A scalable two-stage approach for a class of dimensionality reduction techniques
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Music recommendation by unified hypergraph: combining social media information and music content
Proceedings of the international conference on Multimedia
Ihara coefficients: a flexible tool for higher order learning
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
A polynomial characterization of hypergraphs using the Ihara zeta function
Pattern Recognition
Hypergraph with sampling for image retrieval
Pattern Recognition
Using rich social media information for music recommendation via hypergraph model
ACM Transactions on Multimedia Computing, Communications, and Applications (TOMCCAP) - Special section on ACM multimedia 2010 best paper candidates, and issue on social media
MM '11 Proceedings of the 19th ACM international conference on Multimedia
Graph transduction as a noncooperative game
Neural Computation
Hypergraph based information-theoretic feature selection
Pattern Recognition Letters
Proceedings of the 20th ACM international conference on Multimedia
Hypergraph spectra for semi-supervised feature selection
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
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
News recommendation via hypergraph learning: encapsulation of user behavior and news content
Proceedings of the sixth ACM international conference on Web search and data mining
Image ranking via attribute boosted hypergraph
PCM'12 Proceedings of the 13th Pacific-Rim conference on Advances in Multimedia Information Processing
Understanding and improving relational matrix factorization in recommender systems
Proceedings of the 7th ACM conference on Recommender systems
Hybrid image summarization by hypergraph partition
Neurocomputing
Learning to Recommend Descriptive Tags for Questions in Social Forums
ACM Transactions on Information Systems (TOIS)
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Recently there has been considerable interest in learning with higher order relations (i.e., three-way or higher) in the unsupervised and semi-supervised settings. Hypergraphs and tensors have been proposed as the natural way of representing these relations and their corresponding algebra as the natural tools for operating on them. In this paper we argue that hypergraphs are not a natural representation for higher order relations, indeed pairwise as well as higher order relations can be handled using graphs. We show that various formulations of the semi-supervised and the unsupervised learning problem on hypergraphs result in the same graph theoretic problem and can be analyzed using existing tools.