  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.
