Spherical constraints in the triplet loss function

Learning with a triplet loss function is one of the most common approaches in metric learning. It finds its application in the tasks of image comparison, identification, coding, etc. However, the triplet loss function has a number of disadvantages that can negatively affect quality, such as the tendency of the network to get stuck in local minima and the formation of trivial triplets. This paper proposes a geometric approach to improve quality based on the introduction of an additional term in the loss function. The trajectory change is achieved by redirecting solved and unsolved images to the surfaces of two concentric hyperspheres of different radii. The use of this method helps to reduce the distances between images of the same class. The proposed method does not prevent the use of other modifications of the loss function. It is experimentally shown that the proposed approach makes it possible to reduce the number of unsolved triplets and the number of distant pairs of images of the same class.