  Deep metric learning has been effectively used to learn distance metrics for
different visual tasks like image retrieval, clustering, etc. In order to aid
the training process, existing methods either use a hard mining strategy to
extract the most informative samples or seek to generate hard synthetics using
an additional network. Such approaches face different challenges and can lead
to biased embeddings in the former case, and (i) harder optimization (ii)
slower training speed (iii) higher model complexity in the latter case. In
order to overcome these challenges, we propose a novel approach that looks for
optimal hard negatives (LoOp) in the embedding space, taking full advantage of
each tuple by calculating the minimum distance between a pair of positives and
a pair of negatives. Unlike mining-based methods, our approach considers the
entire space between pairs of embeddings to calculate the optimal hard
negatives. Extensive experiments combining our approach and representative
metric learning losses reveal a significant boost in performance on three
benchmark datasets.
