To achieve a low computational cost when performing online metric learning for large-scale data, we present a one-pass closed-form solution namely OPML in this paper. Typically, the proposed OPML first adopts a one-pass triplet construction strategy, which aims to use only a very small number of triplets to approximate the representation ability of whole original triplets obtained by batch-manner methods. Then, OPML employs a closed-form solution to update the 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 enhance the robustness when in real case the first several samples come from the same class (i.e., cold start problem). In the experiments, we have systematically evaluated our methods (OPML and COPML) on three typical tasks, including UCI data 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 can obtain the promising performance with a very low computational cost. Also, the effectiveness of COPML under the cold start setting is experimentally verified.

本文提出了一种在线度量学习的低计算成本解决方案OPML以及其扩展COPML，其中OPML采用一次三元组构建策略，使用只有很少数量的三元组来近似表示整个原始三元组的表现能力，并采用闭式解来更新新来的样本度量。在UCI数据分类、人脸验证和视频异常事件检测等三个典型任务上进行了实验验证，结果表明OPML和COPML具有良好的性能和非常低的计算成本。

OPML：一种用于在线度量学习的单遍闭式解决方案