  An important challenge in metric learning is scalability to both size and
dimension of input data. Online metric learning algorithms are proposed to
address this challenge. Existing methods are commonly based on (Passive
Aggressive) PA approach. Hence, they can rapidly process large volumes of data
with an adaptive learning rate. However, these algorithms are based on the
Hinge loss and so are not robust against outliers and label noise. Also,
existing online methods usually assume training triplets or pairwise
constraints are exist in advance. However, many datasets in real-world
applications are in the form of input data and their associated labels. We
address these challenges by formulating the online Distance-Similarity learning
problem with the robust Rescaled hinge loss function. The proposed model is
rather general and can be applied to any PA-based online Distance-Similarity
algorithm. Also, we develop an efficient robust one-pass triplet construction
algorithm. Finally, to provide scalability in high dimensional DML
environments, the low-rank version of the proposed methods is presented that
not only reduces the computational cost significantly but also keeps the
predictive performance of the learned metrics. Also, it provides a
straightforward extension of our methods for deep Distance-Similarity learning.
We conduct several experiments on datasets from various applications. The
results confirm that the proposed methods significantly outperform
state-of-the-art online DML methods in the presence of label noise and outliers
by a large margin.
