In metric learning, the goal is to learn an embedding so that data points with the same class are close to each other and data points with different classes are far apart. We propose a distance-ratio-based (DR) formulation for metric learning. Like softmax-based formulation for metric learning, it models $p(y=c|x')$, which is a probability that a query point $x'$ belongs to a class $c$. The DR formulation has two useful properties. First, the corresponding loss is not affected by scale changes of an embedding. Second, it outputs the optimal (maximum or minimum) classification confidence scores on representing points for classes. To demonstrate the effectiveness of our formulation, we conduct few-shot classification experiments using softmax-based and DR formulations on CUB and mini-ImageNet datasets. The results show that DR formulation generally enables faster and more stable metric learning than the softmax-based formulation. As a result, using DR formulation achieves improved or comparable generalization performances.

本研究提出基于距离比率的度量学习公式，该公式拥有两种有用特性，其对嵌入的比例缩放不敏感，同时输出的是生成类别点的最佳分类置信度得分。研究中还通过在CUB和mini-ImageNet数据集上进行少样本分类实验，证明了DR公式通常比softmax公式实现更快和更稳定的度量学习，从而取得了改进或相当的泛化性能。