  In this paper, we revamp the forgotten classical Semi-Supervised Distance
Metric Learning (SSDML) problem from a Riemannian geometric lens, to leverage
stochastic optimization within a end-to-end deep framework. The motivation
comes from the fact that apart from a few classical SSDML approaches learning a
linear Mahalanobis metric, deep SSDML has not been studied. We first extend
existing SSDML methods to their deep counterparts and then propose a new method
to overcome their limitations. Due to the nature of constraints on our metric
parameters, we leverage Riemannian optimization. Our deep SSDML method with a
novel affinity propagation based triplet mining strategy outperforms its
competitors.
