Extracting Shared Subspaces for Multi-label Classification

Multi-label problems arise in various domains such as multitopic web page categorization, protein function prediction, and automated newswire classification. One natural way to deal with such problems is to construct a binary classifier for each label, resulting in a set of independent binary classification problems. Since the multiple labels share the same input space, and the semantics 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 extracting 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, although the optimization 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 framework is that it includes several well-known algorithms as special cases, thus elucidating their intrinsic relationships. We have conducted extensive experiments on eleven multitopic web page categorization tasks, and results demonstrate the effectiveness of the proposed formulation in comparison with several representative algorithms.