In the era of deep learning, loss functions determine the range of tasks available to models and algorithms. To support the application of deep learning in multi-label classification (MLC) tasks, we propose the ZLPR (zero-bounded log-sum-exp \& pairwise rank-based) loss in this paper. Compared to other rank-based losses for MLC, ZLPR can handel problems that the number of target labels is uncertain, which, in this point of view, makes it equally capable with the other two strategies often used in MLC, namely the binary relevance (BR) and the label powerset (LP). Additionally, ZLPR takes the corelation between labels into consideration, which makes it more comprehensive than the BR methods. In terms of computational complexity, ZLPR can compete with the BR methods because its prediction is also label-independent, which makes it take less time and memory than the LP methods. Our experiments demonstrate the effectiveness of ZLPR on multiple benchmark datasets and multiple evaluation metrics. Moreover, we propose the soft version and the corresponding KL-divergency calculation method of ZLPR, which makes it possible to apply some regularization tricks such as label smoothing to enhance the generalization of models.

本文提出了一种基于zero-bounded log-sum-exp和pairwise rank-based的loss function -- ZLPR，能够处理目标标签数量不确定，同时考虑标签之间的相关性，使其具有与二进制关联（BR）和标签功率集（LP）相等的能力，并且可以具有与BR方法相同的计算复杂性和更综合的能力，我们的试验结果显示，ZLPR在多个基准数据集和多个评价指标上都具有优良的效果，并且我们提出了软版本和相应的KL-divergency计算方法的ZLPR，使得可以应用一些正则化技巧来增强模型的泛化性能。

ZLPR：一种多标签分类的新型损失函数