  Multi-label ranking maps instances to a ranked set of predicted labels from
multiple possible classes. The ranking approach for multi-label learning
problems received attention for its success in multi-label classification, with
one of the well-known approaches being pairwise label ranking. However, most
existing methods assume that only partial information about the preference
relation is known, which is inferred from the partition of labels into a
positive and negative set, then treat labels with equal importance. In this
paper, we focus on the unique challenge of ranking when the order of the true
label set is provided. We propose a novel dedicated loss function to optimize
models by incorporating penalties for incorrectly ranked pairs, and make use of
the ranking information present in the input. Our method achieves the best
reported performance measures on both synthetic and real world ranked datasets
and shows improvements on overall ranking of labels. Our experimental results
demonstrate that our approach is generalizable to a variety of multi-label
classification and ranking tasks, while revealing a calibration towards a
certain ranking ordering.
