Hypergraph spectral learning for multi-label classification

Liang Sun, Shuiwang Ji, Jieping Ye

Research output: Chapter in Book/Report/Conference proceedingConference contribution

228 Scopus citations


A hypergraph is a generalization of the traditional graph in which the edges are arbitrary non-empty subsets of the vertex set. It has been applied successfully to capture high-order relations in various domains. In this paper, we propose a hypergraph spectral learning formulation for multi-label classification, where a hypergraph is constructed to exploit the correlation information among different labels. We show that the proposed formulation leads to an eigenvalue problem, which may be computationally expensive especially for large-scale problems. To reduce the computational cost, we propose an approximate formulation, which is shown to be equivalent to a least squares problem under a mild condition. Based on the approximate formulation, efficient algorithms for solving least squares problems can be applied to scale the formulation to very large data sets. In addition, existing regularization techniques for least squares can be incorporated into the model for improved generalization performance. We have conducted experiments using large-scale benchmark data sets, and experimental results show that the proposed hypergraph spectral learning formulation is effective in capturing the high-order relations in multi-label problems. Results also indicate that the approximate formulation is much more efficient than the original one, while keeping competitive classification performance.

Original languageEnglish (US)
Title of host publicationKDD 2008 - Proceedings of the 14th ACMKDD International Conference on Knowledge Discovery and Data Mining
Number of pages9
StatePublished - 2008
Event14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2008 - Las Vegas, NV, United States
Duration: Aug 24 2008Aug 27 2008

Publication series

NameProceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining


Other14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2008
Country/TerritoryUnited States
CityLas Vegas, NV


  • Canonical correlation analysis
  • Efficiency
  • Hypergraph
  • Least squares
  • Multi-label classification
  • Regularization
  • Spectral learning

ASJC Scopus subject areas

  • Software
  • Information Systems


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