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Learning with Hypergraphs: Clustering, Classification, and Embedding

2007

Conference Paper

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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.

Author(s): Zhou, D. and Huang, J. and Schölkopf, B.
Book Title: Advances in Neural Information Processing Systems 19
Journal: Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference
Pages: 1601-1608
Year: 2007
Month: September
Day: 0
Editors: B Sch{\"o}lkopf and J Platt and T Hofmann
Publisher: MIT Press

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: 20th Annual Conference on Neural Information Processing Systems (NIPS 2006)
Event Place: Vancouver, BC, Canada

Address: Cambridge, MA, USA
Digital: 0
ISBN: 0-262-19568-2
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF
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BibTex

@inproceedings{4164,
  title = {Learning with Hypergraphs: Clustering, Classification, and Embedding},
  author = {Zhou, D. and Huang, J. and Sch{\"o}lkopf, B.},
  journal = {Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference},
  booktitle = {Advances in Neural Information Processing Systems 19},
  pages = {1601-1608},
  editors = {B Sch{\"o}lkopf and J Platt and T Hofmann},
  publisher = {MIT Press},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Cambridge, MA, USA},
  month = sep,
  year = {2007},
  month_numeric = {9}
}