A Unified View of Multi-Label Performance Measures

Multi-label classification deals with the problem where each instance is associated with multiple class labels. Because evaluation in multi-label classification is more complicated than single-label setting, a number of performance measures have been proposed. It is noticed that an algorithm usually performs differently on different measures. Therefore, it is important to understand which algorithms perform well on which measure(s) and why. In this paper, we propose a unified margin view to revisit eleven performance measures in multi-label classification. In particular, we define label-wise margin and instance-wise margin, and prove that through maximizing these margins, different corresponding performance measures are to be optimized. Based on the defined margins, a max-margin approach called LIMO is designed and empirical results validate our theoretical findings.