Reduced-rank multi-label classification

Multi-label classification is a natural generalization of the classical binary classification for classifying multiple class labels. It differs from multi-class classification in that the multiple class labels are not exclusive. The key challenge is to improve the classification accuracy by incorporating the intrinsic dependency structure among the multiple class labels. In this article we propose to model the dependency structure via a reduced-rank multi-label classification model, and to enforce a group lasso regularization for sparse estimation. An alternative optimization scheme is developed to facilitate the computation, where a constrained manifold optimization technique and a gradient descent algorithm are alternated to maximize the resultant regularized log-likelihood. Various simulated examples and two real applications are conducted to demonstrate the effectiveness of the proposed method. More importantly, its asymptotic behavior is quantified in terms of the estimation and variable selection consistencies, as well as the model selection consistency via the Bayesian information criterion.