document: Hypergraph spectral learning for multi-label classification 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 .
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