  Deep Metric Learning (DML) is a group of techniques that aim to measure the
similarity between objects through the neural network. Although the number of
DML methods has rapidly increased in recent years, most previous studies cannot
effectively handle noisy data, which commonly exists in practical applications
and often leads to serious performance deterioration. To overcome this
limitation, in this paper, we build a connection between noisy samples and hard
samples in the framework of self-paced learning, and propose a
\underline{B}alanced \underline{S}elf-\underline{P}aced \underline{M}etric
\underline{L}earning (BSPML) algorithm with a denoising multi-similarity
formulation, where noisy samples are treated as extremely hard samples and
adaptively excluded from the model training by sample weighting. Especially,
due to the pairwise relationship and a new balance regularization term, the
sub-problem \emph{w.r.t.} sample weights is a nonconvex quadratic function. To
efficiently solve this nonconvex quadratic problem, we propose a doubly
stochastic projection coordinate gradient algorithm. Importantly, we
theoretically prove the convergence not only for the doubly stochastic
projection coordinate gradient algorithm, but also for our BSPML algorithm.
Experimental results on several standard data sets demonstrate that our BSPML
algorithm has better generalization ability and robustness than the
state-of-the-art robust DML approaches.
