Recent works have revealed an essential paradigm in designing loss functions
that differentiate individual losses vs. aggregate losses. The individual loss
measures the quality of the model on a sample, while the aggregate loss
combines individual losses/scores over each training sample. Both have a common
procedure that aggregates a set of individual values to a single numerical
value. The ranking order reflects the most fundamental relation among
individual values in designing losses. In addition, decomposability, in which a
loss can be decomposed into an ensemble of individual terms, becomes a
significant property of organizing losses/scores. This survey provides a
systematic and comprehensive review of rank-based decomposable losses in
machine learning. Specifically, we provide a new taxonomy of loss functions
that follows the perspectives of aggregate loss and individual loss. We
identify the aggregator to form such losses, which are examples of set
functions. We organize the rank-based decomposable losses into eight
categories. Following these categories, we review the literature on rank-based
aggregate losses and rank-based individual losses. We describe general formulas
for these losses and connect them with existing research topics. We also
suggest future research directions spanning unexplored, remaining, and emerging
issues in rank-based decomposable losses.Comment: Accepted by IEEE Transactions on Pattern Analysis and Machine
Intelligence (TPAMI