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To achieve a low computational cost when performing online metric learningfor large-scale data, we present a one-pass closed-form solution namely OPML inthis paper. Typically, the proposed OPML first adopts a one-pass tripletconstruction strategy, which aims to use only a very small number of tripletsto approximate the representation ability of whole original triplets obtainedby batch-manner methods. Then, OPML employs a closed-form solution to updatethe metric for new coming samples, which leads to a low space (i.e., $O(d)$)and time (i.e., $O(d^2)$) complexity, where $d$ is the feature dimensionality.In addition, an extension of OPML (namely COPML) is further proposed to enhancethe robustness when in real case the first several samples come from the sameclass (i.e., cold start problem). In the experiments, we have systematicallyevaluated our methods (OPML and COPML) on three typical tasks, including UCIdata classification, face verification, and abnormal event detection in videos,which aims to fully evaluate the proposed methods on different sample number,different feature dimensionalities and different feature extraction ways (i.e.,hand-crafted and deeply-learned). The results show that OPML and COPML canobtain the promising performance with a very low computational cost. Also, theeffectiveness of COPML under the cold start setting is experimentally verified.

OPML: A One-Pass Closed-Form Solution for Online Metric Learning