Multi-label problems arise in various domains such as multi-topic document categorization, pro- tein function prediction, and automatic image annotation. One natural way to deal with such problems is to construct a binary classifier for each label, resulting in a set of independent bi- nary classification problems. Since multiple labels share the same input space, and the seman- tics conveyed by different labels are usually correlated, it is essential to exploit the correlation information contained in different labels. In this paper, we consider a general framework for ex- tracting shared structures in multi-label classification. In this framework, a common subspace is assumed to be shared among multiple labels. We show that the optimal solution to the proposed formulation can be obtained by solving a generalized eigenvalue problem, though the problem is nonconvex. For high-dimensional problems, direct computation of the solution is expensive, and we develop an efficient algorithm for this case. One appealing feature of the proposed frame- work is that it includes several well-known algorithms as special cases, thus elucidating their intrinsic relationships. We further show that the proposed framework can be extended to the kernel-induced feature space. We have conducted extensive experiments on multi-topic web page categorization and automatic gene expression pattern image annotation tasks, and results demon- strate the effectiveness of the proposed formulation in comparison with several representative algorithms.
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