  Siamese neural network is a very powerful architecture for both feature
extraction and metric learning. It usually consists of several networks that
share weights. The Siamese concept is topology-agnostic and can use any neural
network as its backbone. The two most popular loss functions for training these
networks are the triplet and contrastive loss functions. In this paper, we
propose two novel loss functions, named Fisher Discriminant Triplet (FDT) and
Fisher Discriminant Contrastive (FDC). The former uses anchor-neighbor-distant
triplets while the latter utilizes pairs of anchor-neighbor and anchor-distant
samples. The FDT and FDC loss functions are designed based on the statistical
formulation of the Fisher Discriminant Analysis (FDA), which is a linear
subspace learning method. Our experiments on the MNIST and two challenging and
publicly available histopathology datasets show the effectiveness of the
proposed loss functions.
