  Recently, deep metric learning techniques received attention, as the learned
distance representations are useful to capture the similarity relationship
among samples and further improve the performance of various of supervised or
unsupervised learning tasks. We propose a novel supervised metric learning
method that can learn the distance metrics in both geometric and probabilistic
space for image recognition. In contrast to the previous metric learning
methods which usually focus on learning the distance metrics in Euclidean
space, our proposed method is able to learn better distance representation in a
hybrid approach. To achieve this, we proposed a Generalized Hybrid Metric Loss
(GHM-Loss) to learn the general hybrid proximity features from the image data
by controlling the trade-off between geometric proximity and probabilistic
proximity. To evaluate the effectiveness of our method, we first provide
theoretical derivations and proofs of the proposed loss function, then we
perform extensive experiments on two public datasets to show the advantage of
our method compared to other state-of-the-art metric learning methods.
