  In multi-label learning, the issue of missing labels brings a major
challenge. Many methods attempt to recovery missing labels by exploiting
low-rank structure of label matrix. However, these methods just utilize global
low-rank label structure, ignore both local low-rank label structures and label
discriminant information to some extent, leaving room for further performance
improvement. In this paper, we develop a simple yet effective discriminant
multi-label learning (DM2L) method for multi-label learning with missing
labels. Specifically, we impose the low-rank structures on all the predictions
of instances from the same labels (local shrinking of rank), and a maximally
separated structure (high-rank structure) on the predictions of instances from
different labels (global expanding of rank). In this way, these imposed
low-rank structures can help modeling both local and global low-rank label
structures, while the imposed high-rank structure can help providing more
underlying discriminability. Our subsequent theoretical analysis also supports
these intuitions. In addition, we provide a nonlinear extension via using
kernel trick to enhance DM2L and establish a concave-convex objective to learn
these models. Compared to the other methods, our method involves the fewest
assumptions and only one hyper-parameter. Even so, extensive experiments show
that our method still outperforms the state-of-the-art methods.
