Metu Loss: Metric Learning With Entangled Triplet Unified Loss

Metric learning aims to define a distance that measures the semantic difference between the instances in a dataset. In this paper, we analyze several well-known triplet loss functions and argue that the gradients of these triplet loss functions do not move the instances in each triplet in the desired direction with the right magnitude. Hence, in order to determine precise interacting forces, we establish a weak analogy with the phenomena of the electromagnetic forces affecting a charged body in free space. Since gradients of the loss function (matching up to the potential energy) with respect to the anchor, positive and negative instances (corresponding to the point charges) of any valid triplet give forces, a loss function can be obtained in a reverse manner, i.e., starting from the desired interacting forces. Based on this idea, we propose a novel triplet loss function, namely, metric learning with entangled triplet unified (METU) loss, that considers the distances between instances in a triplet as well. In order to present only the effect of the loss function, no mining (including the effect of hinge function) is utilized during the experiments. Based on the results on the used fine-grained dataset, CUB-200-2011, it can be concluded that the proposed loss function outperforms the scores of the state-of-the-art methods in the same category.