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Conference Paper

Learning with Hypergraphs: Clustering, Classification, and Embedding

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons84330

Zhou,  D
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83983

Huang,  J
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Zhou, D., Huang, J., & Schölkopf, B. (2007). Learning with Hypergraphs: Clustering, Classification, and Embedding. Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference, 1601-1608.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CBED-8
Abstract
We usually endow the investigated objects with pairwise relationships, which can be illustrated as graphs. In many real-world problems, however, relationships among the objects of our interest are more complex than pairwise. Naively squeezing the complex relationships into pairwise ones will inevitably lead to loss of information which can be expected valuable for our learning tasks however. Therefore we consider using hypergraphs instead to completely represent complex relationships among the objects of our interest, and thus the problem of learning with hypergraphs arises. Our main contribution in this paper is to generalize the powerful methodology of spectral clustering which originally operates on undirected graphs to hypergraphs, and further develop algorithms for hypergraph embedding and transductive classi¯cation on the basis of the spectral hypergraph clustering approach. Our experiments on a number of benchmarks showed the advantages of hypergraphs over usual graphs.