An efficient multi-label support vector machine with a zero label

Existing multi-label support vector machine (Rank-SVM) has an extremely high computational complexity and lacks an intrinsic zero point to determine relevant labels. In this paper, we propose a novel support vector machine for multi-label classification through both simplifying Rank-SVM and adding a zero label, resulting into a quadratic programming problem in which each class has an independent equality constraint. When Frank–Wolfe method is used to solve our quadratic programming problem iteratively, our entire linear programming problem of each step is divided into a series of sub-problems, which dramatically reduces computational cost. It is illustrated that for famous Yeast data set our training procedure runs about 12 times faster than Rank-SVM does under C++ environment. Experiments from five benchmark data sets show that our method is a powerful candidate for multi-label classification, compared with five state-of-the–art multi-label classification techniques.