TY - GEN
T1 - Hypergraph spectral learning for multi-label classification
AU - Sun, Liang
AU - Ji, Shuiwang
AU - Ye, Jieping
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
KW - Canonical correlation analysis
KW - Efficiency
KW - Hypergraph
KW - Least squares
KW - Multi-label classification
KW - Regularization
KW - Spectral learning
UR - http://www.scopus.com/inward/record.url?scp=65449185036&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=65449185036&partnerID=8YFLogxK
U2 - 10.1145/1401890.1401971
DO - 10.1145/1401890.1401971
M3 - Conference contribution
AN - SCOPUS:65449185036
SN - 9781605581934
T3 - Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
SP - 668
EP - 676
BT - KDD 2008 - Proceedings of the 14th ACMKDD International Conference on Knowledge Discovery and Data Mining
T2 - 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2008
Y2 - 24 August 2008 through 27 August 2008
ER -