Multi-label learning with pro loss

Multi-label learning methods assign multiple labels to one object. In practice, in addition to differentiating relevant labels from irrelevant ones, it is often desired to rank the relevant labels for an object, whereas the rankings of irrelevant labels are not important. Such a requirement, however, cannot be met because most existing methods were designed to optimize existing criteria, yet there is no criterion which encodes the aforementioned requirement. In this paper, we present a new criterion, PRO LOSS, concerning the prediction on all labels as well as the rankings of only relevant labels. We then propose ProSVM which optimizes PRO LOSS efficiently using alternating direction method of multipliers. We further improve its efficiency with an upper approximation that reduces the number of constraints from O(T 2) to O(T), where T is the number of labels. Experiments show that our proposals are not only superior on PRO LOSS, but also highly competitive on existing evaluation criteria