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An important challenge in metric learning is scalability to both size anddimension of input data. Online metric learning algorithms are proposed toaddress this challenge. Existing methods are commonly based on (PassiveAggressive) PA approach. Hence, they can rapidly process large volumes of datawith an adaptive learning rate. However, these algorithms are based on theHinge loss and so are not robust against outliers and label noise. Also,existing online methods usually assume training triplets or pairwiseconstraints are exist in advance. However, many datasets in real-worldapplications are in the form of input data and their associated labels. Weaddress these challenges by formulating the online Distance-Similarity learningproblem with the robust Rescaled hinge loss function. The proposed model israther general and can be applied to any PA-based online Distance-Similarityalgorithm. Also, we develop an efficient robust one-pass triplet constructionalgorithm. Finally, to provide scalability in high dimensional DMLenvironments, the low-rank version of the proposed methods is presented thatnot only reduces the computational cost significantly but also keeps thepredictive performance of the learned metrics. Also, it provides astraightforward extension of our methods for deep Distance-Similarity learning.We conduct several experiments on datasets from various applications. Theresults confirm that the proposed methods significantly outperformstate-of-the-art online DML methods in the presence of label noise and outliersby a large margin.

Low-Rank Robust Online Distance/Similarity Learning based on the Rescaled Hinge Loss